Lecture Notes in Computer Science 6146Commenced Publication in 1973Founding and Former Series Editors:Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial BoardDavid Hutchison

Lancaster University, UKTakeo Kanade

Carnegie Mellon University, Pittsburgh, PA, USAJosef Kittler

University of Surrey, Guildford, UKJon M. Kleinberg

Cornell University, Ithaca, NY, USAAlfred Kobsa

University of California, Irvine, CA, USAFriedemann Mattern

ETH Zurich, SwitzerlandJohn C. Mitchell

Stanford University, CA, USAMoni Naor

Weizmann Institute of Science, Rehovot, IsraelOscar Nierstrasz

University of Bern, SwitzerlandC. Pandu Rangan

Indian Institute of Technology, Madras, IndiaBernhard Steffen

TU Dortmund University, GermanyMadhu Sudan

Microsoft Research, Cambridge, MA, USADemetri Terzopoulos

University of California, Los Angeles, CA, USADoug Tygar

University of California, Berkeley, CA, USAGerhard Weikum

Max-Planck Institute of Computer Science, Saarbruecken, Germany

Ying Tan Yuhui Shi Kay Chen Tan (Eds.)

Advancesin Swarm IntelligenceFirst International Conference, ICSI 2010Beijing, China, June 12-15, 2010Proceedings, Part II

13

Volume Editors

Ying TanPeking University, Key Laboratory of Machine Perception (MOE)Department of Machine IntelligenceBeijing 100871, ChinaE-mail: ytan@pku.edu.cn

Yuhui ShiXian Jiaotong-Liverpool University, Research and Postgraduate OfficeSuzhou, 215123, ChinaE-mail: yuhui.shi@xjtlu.edu.cn

Kay Chen TanNational University of SingaporeDepartment of Electrical and Computer Engineering4 Engineering Drive 3, 117576 SingaporeE-mail: eletankc@nus.edu.sg

Library of Congress Control Number: 2010927598

CR Subject Classification (1998): F.1, H.3, I.2, H.4, H.2.8, I.4

LNCS Sublibrary: SL 1 Theoretical Computer Science and General Issues

ISSN 0302-9743ISBN-10 3-642-13497-1 Springer Berlin Heidelberg New YorkISBN-13 978-3-642-13497-5 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting,reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,in its current version, and permission for use must always be obtained from Springer. Violations are liableto prosecution under the German Copyright Law.springer.com

Springer-Verlag Berlin Heidelberg 2010Printed in Germany

Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, IndiaPrinted on acid-free paper 06/3180

Preface

This book and its companion volume, LNCS vols. 6145 and 6146, constitute theproceedings of the International Conference on Swarm Intelligence (ICSI 2010)held in Beijing, the capital of China, during June 12-15, 2010. ICSI 2010 wasthe rst gathering in the world for researchers working on all aspects of swarmintelligence, and provided an academic forum for the participants to disseminatetheir new research ndings and discuss emerging areas of research. It also createda stimulating environment for the participants to interact and exchange infor-mation on future challenges and opportunities of swarm intelligence research.

ICSI 2010 received 394 submissions from about 1241 authors in 22 countriesand regions (Australia, Belgium, Brazil, Canada, China, Cyprus, Hong Kong,Hungary, India, Islamic Republic of Iran, Japan, Jordan, Republic of Korea,Malaysia, Mexico, Norway, Pakistan, South Africa, Chinese Taiwan, UK, USA,Vietnam) across six continents (Asia, Europe, North America, South America,Africa, and Oceania). Each submission was reviewed by at least three reviewers.Based on rigorous reviews by the Program Committee members and reviewers,185 high-quality papers were selected for publication in the proceedings withthe acceptance rate of 46.9%. The papers are organized in 25 cohesive sectionscovering all major topics of swarm intelligence research and development.

In addition to the contributed papers, the ICSI 2010 technical program in-cluded four plenary speeches by Russell C. Eberhart (Indiana University Pur-due University Indianapolis, IUPUI, USA), Gary G. Yen (President of IEEEComputational Intelligence Society, CIS, Oklahoma State University, USA), ErolGelenbe (London Imperial College, UK), Nikola Kasabov (President of Interna-tional Neural Network Soceity, INNS, Auckland University of Technology, NewZealand). Besides the regular parallel oral sessions, ICSI 2010 also had severalposter sessions focusing on wide areas.

As organizers of ICSI 2010, we would like to express sincere thanks to PekingUniversity and Xian Jiaotong-Liverpool University for their sponsorship, to theIEEE Beijing Section, International Neural Network Society, World Federationon Soft Computing, Chinese Association for Articial Intelligence, and NationalNatural Science Foundation of China for their technical co-sponsorship. We ap-preciate the National Natural Science Foundation of China and K.C. Wong Ed-ucation Foundation, Hong Kong, for their nancial and logistic supports.

We would also like to thank the members of the Advisory Committee for theirguidance, the members of the International Program Committee and additionalreviewers for reviewing the papers, and members of the Publications Committeefor checking the accepted papers in a short period of time. Particularly, we aregrateful to the proceedings publisher, Springer, for publishing the proceedings inthe prestigious series of Lecture Notes in Computer Science. Moreover, we wishto express our heartfelt appreciation to the plenary speakers, session chairs, and

VI Preface

student helpers. In addition, there are still many more colleagues, associates,friends, and supporters who helped us in immeasurable ways; we express oursincere gratitude to them all. Last but not the least, we would like to thank allthe speakers, authors and participants for their great contributions that madeICSI 2010 successful and all the hard work worthwhile.

June 2010 Ying TanYuhui Shi

Tan Kay Chen

Organization

Honorary Chairs

Qidi Wu, ChinaRussell C. Eberhart, USA

General Chair

Ying Tan, China

Advisory Committee Chairs

Zhenya He, ChinaXingui He, ChinaXin Yao, UKYixin Zhong, China

Program Committee Chairs

Yuhui Shi, ChinaTan Kay Chen, Singapore

Technical Committee Chairs

Gary G. Yen, USAJong-Hwan Kim, South KoreaXiaodong Li, AustraliaXuelong Li, UKFrans van den Bergh, South Africa

Plenary Sessions Chairs

Robert G. Reynolds, USAQingfu Zhang, UK

Special Sessions Chairs

Martin Middendorf, GermanyJun Zhang, ChinaHaibo He, USA

VIII Organization

Tutorial Chair

Carlos Coello Coello, Mexico

Publications Chair

Zhishun Wang, USA

Publicity Chairs

Ponnuthurai N. Suganthan, SingaporeLei Wang, ChinaMaurice Clerc, France

Finance Chair

Chao Deng, China

Registration Chairs

Huiyun Guo, ChinaYuanchun Zhu, China

Program Committee Members

Peter Andras, UKBruno Apolloni, ItalyPayman Arabshahi, USASabri Arik, TurkeyFrans van den Bergh, South AfricaChristian Blum, SpainSalim Bouzerdoum, AustraliaMartin Brown, UKJinde Cao, ChinaLiang Chen, CanadaZheru Chi, Hong Kong, ChinaLeandro dos Santos Coelho, BrazilCarlos A. Coello Coello, MexicoEmilio Corchado, SpainOscar Cordon, SpainJose Alfredo Ferreira Costa, BrazilXiaohui Cui, USAArindam Das, USA

Prithviraj Dasgupta, USAKusum Deep, IndiaMingcong Deng, JapanYongsheng Ding, ChinaHaibin Duan, ChinaMark Embrechts, USAAndries Engelbrecht, South AfricaMeng Joo Er, SingaporePeter Erdi, USAYoshikazu Fukuyama, JapanWai Keung Fung, CanadaPing Guo, ChinaLuca Maria Gambardella, SwitzerlandErol Gelenbe, UKMongguo Gong, ChinaJivesh Govil, USASuicheng Gu, USAQing-Long Han, Australia

Organization IX

Haibo He, USAZhengguang Hou, ChinaHuosheng Hu, UKXiaohui Hu, USAGuangbin Huang, SingaporeAmir Hussain, UKZhen Ji, ChinaColin Johnson, UKNikola Kasabov, New ZealandArun Khosla, IndiaFranziska Klugl, GermanyLixiang Li, ChinaYangmin Li, Macao, ChinaKang Li, UKXiaoli Li, UKXuelong Li, UKGuoping Liu, UKJu Liu, ChinaFernando Lobo, PortugalChris Lokan, AustraliaWenlian Lu, ChinaHongtao Lu, ChinaWenjian Luo, ChinaXiujun Ma, ChinaJinwen Ma, ChinaBernd Meyer, AustraliaMartin Middendorf, GermanyHongwei Mo, ChinaFrancesco Mondada, SwitzerlandBen Niu, ChinaErkki Oja, FinlandMahamed Omran, KuwaitPaul S. Pang, New ZealandBijaya Ketan Panigrahi, IndiaThomas E. Potok, USA

Jose Principe, USARuhul A. Sarker, AustraliaGerald Schaefer, UKGiovanni Sebastiani, ItalyMichael Small, Hong Kong, ChinaPonnuthurai Nagaratnam Suganthan,

SingaporeNorikazu Takahashi, JapanYing Tan, ChinaRan Tao, ChinaPeter Tino, UKChristos Tjortjis, GreeceG.K. Venayagamoorthy, USALing Wang, ChinaGuoyin Wang, ChinaBing Wang, UKLei Wang, ChinaCheng Xiang, SingaporeShenli Xie, ChinaSimon X. Yang, CanadaYingjie Yang, UKDingli Yu, UKZhigang Zeng, ChinaYanqing Zhang, USAQingfu Zhang, UKJie Zhang, UKLifeng Zhang, ChinaLiangpei Zhang, ChinaJunqi Zhang, ChinaYi Zhang, ChinaJun Zhang, ChinaJinhua Zheng, ChinaAimin Zhou, ChinaZhi-Hua Zhou, China

Reviewers

Ajiboye Saheeb OsunlekeAkira YanouAntonin PonsichBingzhao LiBo LiuCarson K. LeungChangan Jiang

Chen GuiciChing-Hung LeeChonglun FangCong ZhengDawei ZhangDaoqiang ZhangDong Li

X Organization

Fei GeFeng JiangGan HuangGang ChenHaibo BaoHongyan WangHugo HernandezI-Tung YangIbanez PanizoJackson GomesJanyl JumadinovaJin HuJin XuJing DengJuan ZhaoJulio BarreraJun GuoJun ShenJun WangKe ChengKe DingKenya JinnoLiangpei ZhangLihua JiangLili WangLin WangLiu LeiLixiang LiLorenzo ValerioNaoki OnoNi BuOrlando CoelhoOscar IbanezPengtao Zhang

Prakash ShelokarQiang LuQiang SongQiao CaiQingshan LiuQun NiuRenato SassiSatvir SinghSergio P. SantosSheng ChenShuhui BiSimone BassisSong ZhuSpiros DenaxasStefano BenedettiniStelios TimotheouTakashi TanizakiUsman AdeelValerio ArnaboldiWangli HeWei WangWen ShengjunWenwu YuX.M. ZhangXi HuangXiaolin LiXin GengXiwei LiuYan YangYanqiao ZhuYongqing YangYongsheng DongYulong WangYuan Cao

Table of Contents Part II

Fuzzy Methods

On the Correlations between Fuzzy Variables . . . . . . . . . . . . . . . . . . . . . . . . 1Yankui Liu and Xin Zhang

Modeling Fuzzy Data Envelopment Analysis with ExpectationCriterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Xiaodong Dai, Ying Liu, and Rui Qin

Finding and Evaluating Fuzzy Clusters in Networks . . . . . . . . . . . . . . . . . . 17Jian Liu

On Fuzzy Diagnosis Model of Planes Revolution Swing Fault andSimulation Researches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Dongcai Qu, Jihong Cheng, Wanli Dong, and Ruizhi Zhang

Fuzzy Cluster Centers Separation Clustering Using PossibilisticApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Xiaohong Wu, Bin Wu, Jun Sun, Haijun Fu, and Jiewen Zhao

A Class of Fuzzy Portfolio Optimization Problems: E-S Models . . . . . . . . 43Yankui Liu and Xiaoli Wu

Application of PSO-Adaptive Neural-Fuzzy Inference System (ANFIS)in Analog Circuit Fault Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Lei Zuo, Ligang Hou, Wang Zhang, Shuqin Geng, and Wucheng Wu

Applications of Computational IntelligenceAlgorithms

Chaos Optimization SVR Algorithm with Application in Prediction ofRegional Logistics Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Haiyan Yang, Yongquan Zhou, and Hongxia Liu

Cooperation Partners Selection for Multiple-Core-Type MPN . . . . . . . . . . 65Shuili Yang, Taofen Li, and Yu Dong

A New Technique for Forecast of Surface Runo . . . . . . . . . . . . . . . . . . . . . 71Lihua Feng and Juhua Zheng

Computational Intelligence Algorithms Analysis for Smart Grid CyberSecurity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Yong Wang, Da Ruan, Jianping Xu, Mi Wen, and Liwen Deng

XII Table of Contents Part II

Using AOBP for Denitional Question Answering . . . . . . . . . . . . . . . . . . . . 85Junkuo Cao, Weihua Wang, and Yuanzhong Shu

Radial Basis Function Neural Network Based on PSO with MutationOperation to Solve Function Approximation Problem . . . . . . . . . . . . . . . . . 92

Xiaoyong Liu

CRPSO-Based Integrate-and-Fire Neuron Model for Time SeriesPrediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Liang Zhao and Feng Qian

An Agent-Based Model of Make-to-Order Supply Chains . . . . . . . . . . . . . . 108Jing Li and Zhaohan Sheng

Signal Processing and Information Security

Pricing and Bidding Strategy in AdWords Auction under HeterogeneousProducts Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

E. Zhang and Yiqin Zhuo

FIR Cuto Frequency Calculating for ECG Signal Noise RemovingUsing Articial Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Sara Moein

A System Identication Using DRNN Based on Swarm Intelligence . . . . . 132Qunzhou Yu, Jian Guo, and Cheng Zhou

Force Identication by Using SVM and CPSO Technique . . . . . . . . . . . . . . 140Zhichao Fu, Cheng Wei, and Yanlong Yang

A Novel Dual Watermarking Scheme for Audio Copyright Protectionand Content Authentication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Zhaoyang Ma, Xueying Zhang, and Jinxia Yang

On the Strength Evaluation of Lesamnta against DierentialCryptanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Yasutaka Igarashi and Toshinobu Kaneko

Information Processing System

Sparse Source Separation with Unknown Source Number . . . . . . . . . . . . . . 167Yujie Zhang, Hongwei Li, and Rui Qi

Matrix Estimation Based on Normal Vector of Hyperplane in SparseComponent Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Feng Gao, Gongxian Sun, Ming Xiao, and Jun Lv

Table of Contents Part II XIII

A New HOS-Based Blind Source Extraction Method to Extract Rhythms from EEG Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Kun Cai and Shengli Xie

An Adaptive Sampling Target Tracking Method of WMSNs . . . . . . . . . . . 188Shikun Tian, Xinyu Jin, and Yu Zhang

Asymptotic Equivalent Analysis for LTI Overlapping Large-ScaleSystems and Their Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Qian Wang and Xuebo Chen

Brain-Computer Interface System Using Approximate Entropy andEMD Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

Qiwei Shi, Wei Zhou, Jianting Cao, Toshihisa Tanaka, andRubin Wang

An Application of LFP Method for Sintering Ore Ratio . . . . . . . . . . . . . . . 213Xi Cheng, Kailing Pan, and Yunfeng Ma

Contour Map Plotting Algorithm for Evaluating Characteristics ofTransient Electron Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Chunlong Shen, Miping Zhang, Kehong Wang, Yong Peng, andJianhua Xu

Study on Modication Coecient of Planetary Gear . . . . . . . . . . . . . . . . . . 229Tao Zhang and Lei Zhu

Intelligent Control

The Automatic Feed Control Based on OBP Neural Network . . . . . . . . . . 236Ding Feng, Bianyou Tan, Peng Wang, Shouyong Li, Jin Liu,Cheng Yang, Yongxin Yuan, and Guanjun Xu

A Capacitated Production Planning Problem for Closed-Loop SupplyChain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

Jian Zhang and Xiao Liu

Distributed Hierarchical Control for Railway Passenger-Dedicated LineIntelligent Transportation System Based on Multi-Agent . . . . . . . . . . . . . . 252

Jingdong Sun, Yao Wang, and Shan Wang

GA-Based Integral Sliding Mode Control for AGC . . . . . . . . . . . . . . . . . . . 260Dianwei Qian, Xiangjie Liu, Miaomiao Ma, and Chang Xu

Stable Swarm Formation Control Using Onboard Sensor Information . . . 268Viet-Hong Tran and Suk-Gyu Lee

XIV Table of Contents Part II

A Distributed Energy-aware Trust Topology Control Algorithm forService-Oriented Wireless Mesh Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Chuanchuan You, Tong Wang, BingYu Zhou, Hui Dai, andBaolin Sun

A Quay Crane Scheduling Model in Container Terminals . . . . . . . . . . . . . . 283Qi Tang

Leader-Follower Formation Control of Multi-robots by Using a StableTracking Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

Yanyan Dai, Viet-Hong Tran, Zhiguang Xu, and Suk-Gyu Lee

Research on the Coordination Control of Vehicle EPS and ABS . . . . . . . . 299Weihua Qin, Qidong Wang, Wuwei Chen, and Shenghui Pan

Classier Systems

SVM Classier Based Feature Selection Using GA, ACO and PSO forsiRNA Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Yamuna Prasad, K. Kanad Biswas, and Chakresh Kumar Jain

A Discrete-Time Recurrent Neural Network for Solving Systems ofComplex-Valued Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

Wudai Liao, Jiangfeng Wang, and Junyan Wang

A Recurrent Neural Network for Solving Complex-Valued QuadraticProgramming Problems with Equality Constraints . . . . . . . . . . . . . . . . . . . 321

Wudai Liao, Jiangfeng Wang, and Junyan Wang

Computer-Aided Detection and Classication of Masses in DigitizedMammograms Using Articial Neural Network . . . . . . . . . . . . . . . . . . . . . . . 327

Mohammed J. Islam, Majid Ahmadi, and Maher A. Sid-Ahmed

Gene Selection and PSO-BP Classier Encoding a Prior Information . . . 335Yu Cui, Fei Han, and Shiguang Ju

A Modied D-S Decision-Making Algorithm for Multi-sensor TargetIdentication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

Xiaolong Liang, Jinfu Feng, and An Liu

Machine Learning Methods

Intelligent Decision Support System for Breast Cancer . . . . . . . . . . . . . . . . 351R.R. Janghel, Anupam Shukla, Ritu Tiwari, and Rahul Kala

An Automatic Index Validity for Clustering . . . . . . . . . . . . . . . . . . . . . . . . . 359Zizhu Fan, Xiangang Jiang, Baogen Xu, and Zhaofeng Jiang

Table of Contents Part II XV

Exemplar Based Laplacian Discriminant Projection . . . . . . . . . . . . . . . . . . 367X.G. Tu and Z.L. Zheng

A Novel Fast Non-negative Matrix Factorization Algorithm and ItsApplication in Text Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

Fang Li and Qunxiong Zhu

Coordination of Urban Intersection Agents Based on Multi-interactionHistory Learning Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Xinhai Xia and Lunhui Xu

Global Exponential Stability Analysis of a General Class of HopeldNeural Networks with Distributed Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

Chaojin Fu, Wei Liu, and Meng Yang

Object Recognition of a Mobile Robot Based on SIFT with De-speckleFiltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Zhiguang Xu, Kyung-Sik Choi, Yanyan Dai, and Suk-Gyu Lee

Some Research on Functional Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 406Hui Liu

Other Optimization Algorithms

Optimization Algorithm of Scheduling Six Parallel Activities to ThreePairs Order Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

Xiuhua Zhao, Jianxun Qi, Shisen Lv, and Zhixiong Su

Research on the Optimization Decision-Making TwoRow-Sequencing-Pairs of Activities with Slacks . . . . . . . . . . . . . . . . . . . . . . 422

Shisen Lv, Jianxun Qi, Xiuhua Zhao, and Zhixiong Su

A Second-Order Modied Version of Mehrotra-type Predictor-CorrectorAlgorithm for Convex Quadratic Optimization . . . . . . . . . . . . . . . . . . . . . . . 430

Qiang Hu and Mingwang Zhang

An Optimization Algorithm of Spare Capacity Allocation by DynamicSurvivable Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Zuxi Wang, Li Li, Gang Sun, and Hanping Hu

Numerical Approximation and Optimum Method of ProductionMonitoring System of the Textile Enterprise . . . . . . . . . . . . . . . . . . . . . . . . . 446

Jingfeng Shao, Zhanyi Zhao, Liping Yang, and Peng Song

Design and Simulation of Simulated Annealing Algorithm withHarmony Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

Hua Jiang, Yanxiu Liu, and Liping Zheng

XVI Table of Contents Part II

Sudoku Using Parallel Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . 461Zahra Karimi-Dehkordi, Kamran Zamanifar,Ahmad Baraani-Dastjerdi, and Nasser Ghasem-Aghaee

Data Mining Methods

A Novel Spatial Obstructed Distance by Dynamic Piecewise LinearChaotic Map and Dynamic Nonlinear PSO . . . . . . . . . . . . . . . . . . . . . . . . . . 468

Xueping Zhang, Yawei Liu, Jiayao Wang, and Haohua Du

A Novel Spatial Clustering with Obstacles Constraints Based onPNPSO and K-Medoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

Xueping Zhang, Haohua Du, Tengfei Yang, and Guangcai Zhao

The Optimization of Procedure Chain of Three Activities with a RelaxQuantum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

Shisen Lv, Jianxun Qi, and Xiuhua Zhao

Invalidity Analysis of Eco-compensation Projects Based on Two-StageGame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

Xianjia Wang, Nan Xu, and Binbin Huang

Intelligent Computing Methods and Applications

Botnet Trac Discriminatory Analysis Using Particle SwarmOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

Yan Zhang, Shuguang Huang, Yongyi Wang, and Min Zhang

Design and Implement of a Scheduling Strategy Based on PSOAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

Suqin Liu, Jing Wang, Xingsheng Li, Jun Shuo, and Huihui Liu

Optimal Design for 2-DOF PID Regulator Based on PSO Algorithm . . . 515Haiwen Wang, Jinggang Zhang, Yuewei Dai, and Junhai Qu

An Examination on Emergence from Social Behavior: A Case inInformation Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

Daren Li, Muyun Yang, Sheng Li, and Tiejun Zhao

A Novel Fault Diagnosis Method Based-on Modied Neural Networksfor Photovoltaic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Kuei-Hsiang Chao, Chao-Ting Chen, Meng-Hui Wang, andChun-Fu Wu

Wavelet Packet and Generalized Gaussian Density Based TextilePattern Classication Using BP Neural Network . . . . . . . . . . . . . . . . . . . . . 540

Yean Yin, Liang Zhang, Miao Jin, and Sunyi Xie

Table of Contents Part II XVII

Air Quality Prediction in Yinchuan by Using Neural Networks . . . . . . . . . 548Fengjun Li

Application of Articial Neural Network in Composite Research . . . . . . . 558Peixian Zhu, Shenggang Zhou, Jie Zhen, and Yuhui Li

Application of Short-Term Load Forecasting Based on ImprovedGray-Markov Residuals Amending of BP Neural Network . . . . . . . . . . . . . 564

Dongxiao Niu, Cong Xu, Jianqing Li, and Yanan Wei

The RBFNNs Application in Nonlinear System Model Based onImproved APC-III Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

Xinping Liu, Xiwen Xue, and Mingwen Zheng

An Improved Harmony Search Algorithm with Dynamic Adaptationfor Location of Critical Slip Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576

Shibao Lu, Weijuan Meng, and Liang Li

Verifying Election Campaign Optimization Algorithm by SeveralBenchmarking Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

Wenge Lv, Qinghua Xie, Zhiyong Liu, Deyuan Li, Siyuan Cheng,Shaoming Luo, and Xiangwei Zhang

Data Mining Algorithms and Applications

An Algorithm of Alternately Mining Frequent Neighboring Class Set . . . 588Gang Fang

Internet Public Opinion Hotspot Detection Research Based on K-meansAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

Hong Liu and Xiaojun Li

A Trac Video Background Extraction Algorithm Based on ImageContent Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603

Bo Qin, Jingjing Wang, Jian Gao, Titi Pang, and Fang Su

A Novel Clustering and Verication Based Microarray DataBi-clustering Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

Yanjie Zhang, Hong Wang, and Zhanyi Hu

FCM Clustering Method Based Research on the FluctuationPhenomenon in Power Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

Huiqiong Deng, Weilu Zhu, Shuai Wang, Keju Sun,Yanming Huo, and Lihua Sun

A Multimodality Medical Image Fusion Algorithm Based on WaveletTransform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

Jionghua Teng, Xue Wang, Jingzhou Zhang, Suhuan Wang, andPengfei Huo

XVIII Table of Contents Part II

Adjusting the Clustering Results Referencing an External Set . . . . . . . . . 634Baojia Li, Yongqian Liu, and Mingzhu Liu

Sensitivity Analysis on Single Activity to Network Float in CPMNetwork Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

Zhixiong Su and Jianxun Qi

Research on Hand Language Video Retrieval . . . . . . . . . . . . . . . . . . . . . . . . 648Shilin Zhang and Mei Gu

Other Applications

Research on Preprocess Approach for Uncertain System Based onRough Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

Xu E, Lijin Fan, Sheng Li, Jiaxin Yang, Hao Wu, Tao Qu, andHaijun Mu

Research on the Synergy Model between Knowledge Capital andRegional Economic Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664

Cisheng Wu and Meng Song

Research on Benets Distribution Model for Maintenance Partnershipsof the Single-Core MPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672

Taofen Li, Shuili Yang, and Yao Yao

Illumination Invariant Color Model for Object Recognition in RobotSoccer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680

Xin Luan, Weiwei Qi, Dalei Song, Ming Chen, Tieyi Zhu, andLi Wang

A New Algorithm of an Improved Detection of Moving Vehicles . . . . . . . . 688Huanglin Zeng and Zhenya Wang

An Improved Combination of Constant Modulus Algorithms Used inUnderwater Acoustic Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694

Xiaoling Ning, Zhong Liu, and Yasong Luo

PID Control Analysis of Brake Test Bench . . . . . . . . . . . . . . . . . . . . . . . . . . 701Rui Zhang, Haiyin Li, and Huimin Xiao

The Dual Model of a Repairable System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708Yunfei Guo, Maosheng Lai, and Zhe Yin

A Comprehensive Study of Neutral-Point-Clamped Voltage SourcePWM Rectiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718

Guojun Tan, Zongbin Ye, Yuan Li, Yaofei Han, and Wei Jing

FPGA-Based Cooling Fan Control System for Automobile Engine . . . . . . 728Meihua Xu, Fangjie Zhao, and Lianzhou Wang

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737

Table of Contents Part I

Theoretical Analysis of Swarm IntelligenceAlgorithms

Stability Problem for a Predator-Prey System . . . . . . . . . . . . . . . . . . . . . . . 1Zvi Retchkiman Konigsberg

Study on the Local Search Ability of Particle Swarm Optimization . . . . . 11Yuanxia Shen and Guoyin Wang

The Performance Measurement of a Canonical Particle SwarmOptimizer with Diversive Curiosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Hong Zhang and Jie Zhang

Mechanism and Convergence of Bee-Swarm Genetic Algorithm . . . . . . . . 27Di Wu, Rongyi Cui, Changrong Li, and Guangjun Song

On the Farther Analysis of Performance of the Articial SearchingSwarm Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Tanggong Chen, Lijie Zhang, and Lingling Pang

Orthogonality and Optimality in Non-Pheromone Mediated Foraging . . . 42Sanza Kazadi, James Yang, James Park, and Andrew Park

An Adaptive Staged PSO Based on Particles Search Capabilities . . . . . . 52Kun Liu, Ying Tan, and Xingui He

PSO Algorithms

A New Particle Swarm Optimization Algorithm and Its NumericalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Yuelin Gao, Fanfan Lei, and Miaomiao Wang

A New PSO Model Mimicking Bio-parasitic Behavior . . . . . . . . . . . . . . . . . 68Quande Qin, Rongjun Li, Ben Niu, and Li Li

KNOB Particle Swarm Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Junqi Zhang, Kun Liu, and Ying Tan

Grouping-Shuing Particle Swarm Optimization: An Improved PSOfor Continuous Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Yinghai Li, Xiaohua Dong, and Ji Liu

Gender-Hierarchy Particle Swarm Optimizer Based on Punishment . . . . . 94Jiaquan Gao, Hao Li, and Luoke Hu

XX Table of Contents Part I

An Improved Probability Particle Swarm Optimization Algorithm . . . . . . 102Qiang Lu and Xuena Qiu

An Automatic Niching Particle Swarm for Multimodal FunctionOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Yu Liu, Zhaofa Yan, Wentao Li, Mingwei Lv, and Yuan Yao

An Availability-Aware Task Scheduling for Heterogeneous SystemsUsing Quantum-behaved Particle Swarm Optimization . . . . . . . . . . . . . . . . 120

Hao Yuan, Yong Wang, and Long Chen

A Novel Encoding Scheme of PSO for Two-Machine GroupScheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Cheng-Dar Liou and Chun-Hung Liu

Improved Quantum Particle Swarm Optimization by Bloch Sphere . . . . . 135Yu Du, Haibin Duan, Renjie Liao, and Xihua Li

An Improved Particle Swarm Optimization for Permutation FlowshopScheduling Problem with Total Flowtime Criterion . . . . . . . . . . . . . . . . . . . 144

Xianpeng Wang and Lixin Tang

Applications of PSO Algorithms

Broadband MVDR Beamformer Applying PSO . . . . . . . . . . . . . . . . . . . . . . 152Liang Wang and Zhijie Song

Medical Image Registration Algorithm with Generalized MutualInformation and PSO-Powell Hybrid Algorithm . . . . . . . . . . . . . . . . . . . . . . 160

Jingzhou Zhang, Pengfei Huo, Jionghua Teng, Xue Wang, andSuhuan Wang

Particle Swarm Optimization for Automatic Selection of RelevanceFeedback Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Peng-Yeng Yin

Performance of Optimized Fuzzy Edge Detectors Using Particle SwarmAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Noor Elaiza Abdul Khalid and Mazani Manaf

PSO Heuristics Algorithm for Portfolio Optimization . . . . . . . . . . . . . . . . . 183Yun Chen and Hanhong Zhu

A New Particle Swarm Optimization Solution to Nonconvex EconomicDispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Jianhua Zhang, Yingxin Wang, Rui Wang, and Guolian Hou

Optimal Micro-siting of Wind Farms by Particle SwarmOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Chunqiu Wan, Jun Wang, Geng Yang, and Xing Zhang

Table of Contents Part I XXI

PSO Applied to Table Allocation Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 206David A. Braude and Anton van Wyk

Finding the Maximum Module of the Roots of a Polynomial by ParticleSwarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Liangdong Qu and Dengxu He

ACO Algorithms

Research on the Ant Colony Optimization Algorithm withMulti-population Hierarchy Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Xuzhi Wang, Jing Ni, and Wanggen Wan

Graph Partitioning Using Improved Ant Clustering . . . . . . . . . . . . . . . . . . . 231M. Sami Soliman and Guanzheng Tan

A Knowledge-Based Ant Colony Optimization for a Grid WorkowScheduling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Yanli Hu, Lining Xing, Weiming Zhang, Weidong Xiao, andDaquan Tang

An Improved Parallel Ant Colony Optimization Based on MessagePassing Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Jie Xiong, Xiaohong Meng, and Caiyun Liu

Applications of ACO Algorithms

Research on Fault Diagnosis Based on BP Neural Network Optimizedby Chaos Ant Colony Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

Liuyi Ling, Yourui Huang, and Liguo Qu

Edge Detection of Laser Range Image Based on a Fast Adaptive AntColony Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

Yonghua Wu, Yihua Hu, Wuhu Lei, Nanxiang Zhao, and Tao Huang

A Real-Time Moving Ant Estimator for Bearings-Only Tracking . . . . . . . 273Jihong Zhu, Benlian Xu, Fei Wang, and Zhiquan Wang

Two-Stage Inter-Cell Layout Design for Cellular Manufacturing byUsing Ant Colony Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 281

Bo Xing, Wen-jing Gao, Fulufhelo V. Nelwamondo,Kimberly Battle, and Tshilidzi Marwala

Images Boundary Extraction Based on Curve Evolution and AntColony Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

JinJiang Li, Da Yuan, Zhen Hua, and Hui Fan

ACO Based Energy-Balance Routing Algorithm for WSNs . . . . . . . . . . . . 298Xuepeng Jiang and Bei Hong

XXII Table of Contents Part I

Swarm Intelligence Algorithms for Portfolio Optimization . . . . . . . . . . . . . 306Hanhong Zhu, Yun Chen, and Kesheng Wang

Articial Immune System

Document Classication with Multi-layered Immune Principle . . . . . . . . . 314Chunlin Liang, Yindie Hong, Yuefeng Chen, and Lingxi Peng

A Quantum Immune Algorithm for Multiobjective Parallel MachineScheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

Zhiming Fang

A Resource Limited Immune Approach for Evolving Architecture andWeights of Multilayer Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Xiaoyang Fu, Shuqing Zhang, and Zhenping Pang

Cryptanalysis of Four-Rounded DES Using Binary Articial ImmuneSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

Syed Ali Abbas Hamdani, Sarah Shaq, and Farrukh Aslam Khan

An Immune Concentration Based Virus Detection Approach UsingParticle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Wei Wang, Pengtao Zhang, and Ying Tan

Novel Swarm-Based Optimization Algorithms

Fireworks Algorithm for Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355Ying Tan and Yuanchun Zhu

Bacterial Foraging Optimization Algorithm with Particle SwarmOptimization Strategy for Distribution Network Reconguration . . . . . . . 365

Tianlei Zang, Zhengyou He, and Deyi Ye

Optimization Design of Flash Structure for Forging Die Based onKriging-PSO Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Yu Zhang, Zhiguo An, and Jie Zhou

A Scatter Search Algorithm for the Slab Stack Shuing Problem . . . . . . 382Xu Cheng and Lixin Tang

Collaboration Algorithm of FSMAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390Qingshan Li, Dan Jiang, Haishun Yun, and He Liu

GPU-Based Parallelization Algorithm for 2D Line IntegralConvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Bo Qin, Zhanbin Wu, Fang Su, and Titi Pang

Biogeography Migration Algorithm for Traveling Salesman Problem . . . . 405Hongwei Mo and Lifang Xu

Table of Contents Part I XXIII

An Approach of Redistricting Based on Simple and Compactness . . . . . . 415Shanchen Pang, Hua He, Yicheng Li, Tian Zhou, andKangzheng Xing

Genetic Algorithms

A Rapid Chaos Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425Jian Gao, Ming Xiao, and Wei Zhang

Fitness Function of Genetic Algorithm in Structural ConstraintOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

Xinchi Yan and Xiaohan Wang

Using Genetic Algorithm for Classication in Face Recognition . . . . . . . . 439Xiaochuan Zhao

Dynamic Path Optimization of Emergency Transport Based onHierarchical Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

Yongjie Ma, Ye Tian, and Wenjing Hou

Fault Diagnosis of Analog Circuits Using Extension GeneticAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

Meng-Hui Wang, Kuei-Hsiang Chao, and Yu-Kuo Chung

A Collision Detection Algorithm Based on Self-adaptive GeneticMethod in Virtual Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

Jue Wu, Lixue Chen, Lei Yang, Qunyan Zhang, and Lingxi Peng

A Non-dominated Sorting Bit Matrix Genetic Algorithm for P2P RelayOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

Qian He, Junliang Chen, Xiangwu Meng, and Yanlei Shang

Fast Parallel Memetic Algorithm for Vector Quantization Based forRecongurable Hardware and Softcore Processor . . . . . . . . . . . . . . . . . . . . . 479

Tsung-Yi Yu, Wen-Jyi Hwang, and Tsung-Che Chiang

Evolutionary Computation

Optimization of Minimum Completion Time MTSP Based on theImproved DE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

Huiren Zhou and Yinghui Wei

Dierential Evolution for Optimization of Land Use . . . . . . . . . . . . . . . . . . 499Yanjie Zhu and Zhihui Feng

Hybrid Dierential Evolution for Knapsack Problem . . . . . . . . . . . . . . . . . . 505Changshou Deng, Bingyan Zhao, Yanling Yang, and Anyuan Deng

XXIV Table of Contents Part I

Bottom-Up Tree Evaluation in Tree-Based Genetic Programming . . . . . . 513Geng Li and Xiao-jun Zeng

Solving Vehicle Assignment Problem Using EvolutionaryComputation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

Marina Yuso, Junaidah Arin, and Azlinah Mohamed

A Computerized Approach of the Knowledge Representation of DigitalEvolution Machines in an Articial World . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

Istvan Elek

An Improved Thermodynamics Evolutionary Algorithm Based on theMinimal Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

Fahong Yu, Yuanxiang Li, and Weiqin Ying

Hybrid Algorithms

A Hybrid Evolutionary Algorithm Based on Alopex and Estimation ofDistribution Algorithm and Its Application for Optimization . . . . . . . . . . 549

Shaojun Li, Fei Li, and Zhenzhen Mei

A Hybrid Swarm Intelligent Method Based on Genetic Algorithm andArticial Bee Colony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

Haiyan Zhao, Zhili Pei, Jingqing Jiang, Renchu Guan,Chaoyong Wang, and Xiaohu Shi

A Hybrid PSO/GA Algorithm for Job Shop Scheduling Problem . . . . . . . 566Jianchao Tang, Guoji Zhang, Binbin Lin, and Bixi Zhang

A Hybrid Particle Swarm Optimization Algorithm for Order PlanningProblems of Steel Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574

Tao Zhang, Zhifang Shao, Yuejie Zhang, Zhiwang Yu, andJianlin Jiang

Hybrid Particle Swarm and Conjugate Gradient OptimizationAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

Abdallah Qteish and Mohammad Hamdan

A Hybrid of Particle Swarm Optimization and Local Search forMultimodal Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589

Jin Qin, Yixin Yin, and Xiaojuan Ban

A Cooperative Ant Colony System and Genetic Algorithm for TSPs . . . . 597Gaifang Dong and William W. Guo

Tracking Control of Uncertain DC Server Motors Using Genetic FuzzySystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

Wei-Min Hsieh, Yih-Guang Leu, Hao-Cheng Yang, and Jian-You Lin

Table of Contents Part I XXV

Multi-Objective Optimization Algorithms

Novel Multi-Objective Genetic Algorithm Based on Static BayesianGame Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612

Zhiyong Li, Dong Chen, Ahmed Sallam, and Li Zhao

A Hybrid Pareto-Based Tabu Search for Multi-objective Flexible JobShop Scheduling Problem with E/T Penalty . . . . . . . . . . . . . . . . . . . . . . . . . 620

Junqing Li, Quanke Pan, Shengxian Xie, and Jing Liang

Research on Multi-objective Optimization Design of the UUV ShapeBased on Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628

Baowei Song, Qifeng Zhu, and Zhanyi Liu

Multi-Objective Optimization for Massive Pedestrian Evacuation UsingAnt Colony Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636

Xinlu Zong, Shengwu Xiong, Zhixiang Fang, and Qiuping Li

An Improved Immune Genetic Algorithm for MultiobjectiveOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643

Guixia He, Jiaquan Gao, and Luoke Hu

Multi-robot Systems

Enhanced Mapping of Multi-robot Using Distortion Reducing FilterBased SIFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

Kyung-Sik Choi, Yoon-Gu Kim, Jinung An, and Suk-Gyu Lee

Study on Improved GPGP-Based Multi-agent SemiconductorFabrication Line Dynamic Scheduling Method . . . . . . . . . . . . . . . . . . . . . . . 659

Xin Ma and Ying He

Multi-robot Formation Control Using Reinforcement LearningMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

Guoyu Zuo, Jiatong Han, and Guansheng Han

Development of Image Stabilization System Using Extended KalmanFilter for a Mobile Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

Yun Won Choi, Tae Hun Kang, and Suk Gyu Lee

Multi-agent Based Complex Systems

Diusing Method for Unknown Environment Exploration in MultiRobot Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683

Dilshat Saitov, Ki Joon Han, and Suk-Gyu Lee

Impulsive Consensus Seeking in Delayed Networks of Multi-agents . . . . . 691Quanjun Wu, Lan Xiang, and Jin Zhou

XXVI Table of Contents Part I

The Application of Multi-agent Technology on the Level of RepairAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699

Xiangkai Liu, Yanfeng Tang, Lin Zheng, Bingfeng Zhu, andJianing Wang

The Framework of an Intelligent Battleeld Damage AssessmentSystem Based on Multi-Agent System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707

Xiangkai Liu, Huimei Li, Jian Zhang, Jianing Wang, andWenhua Xing

Adaptive System of Heterogeneous Multi-agent Investors in an ArticialEvolutionary Double Auction Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715

Chi Xu, Xiaoyu Zhao, and Zheru Chi

Average Consensus for Directed Networks of Multi-agent withTime-Varying Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723

Tiecheng Zhang and Hui Yu

Multi-Agent Cooperative Reinforcement Learning in 3D VirtualWorld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731

Ping Zhang, Xiujun Ma, Zijian Pan, Xiong Li, and Kunqing Xie

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741

On the Correlations between Fuzzy Variables

Yankui Liu and Xin Zhang

College of Mathematics and Computer Science, Hebei UniversityBaoding 071002, Hebei, China

yliu@hbu.edu.cn, xinzhang08@126.com

Abstract. The expected value and variance of a fuzzy variable havebeen well studied in the literature, and they provide important charac-terizations of the possibility distribution for the fuzzy variable. In thispaper, we seek a similar characterization of the joint possibility distribu-tion for a pair of fuzzy variables. In view of the success of introducing theexpected value and variance as fuzzy integrals of appropriate functions ofsingle fuzzy variable, it is natural to look to fuzzy integrals of appropriatefunctions of a pair of fuzzy variables. We consider one such function toobtain the covariance of the pair fuzzy variables and focus on its compu-tation for common possibility distributions. Under mild assumptions, wederive several useful covariance formulas for triangular and trapezoidalfuzzy variables, which have potential applications in quantitative nanceproblems when we consider the correlations among fuzzy returns.

Keywords: Fuzzy variable, Expected value, Covariance, Quantitativenance problem.

1 Introduction

In probability theory, the mean value of a random variable locates the centerof the induced probability distribution, which provides important informationabout the distribution. Since quite dierent probability distributions may sharethe same mean value, we can distinguish them via variance. Therefore, boththe mean value and the variance provide useful characterizations of the prob-ability distribution for a single random variable. To show the probabilistic tiesbetween a pair of random variables, the covariance is a practical tool and hasbeen widely studied in the literature. Chen et al. [1] proposed a simulation al-gorithm to estimate mean, variance, and covariance for a set of order statisticsfrom inverse-Gaussian distribution; Cuadras [2] gave the covariance between thefunctions of two random variables in terms of the cumulative distribution func-tions; Hirschberger et al. [3] developed a procedure for the random generationof covariance matrices in portfolio selection. For more applications about thecovariance, the interested reader may refer to [4,5].

Since the pioneering work of Zadeh [6], possibility theory has been well de-veloped and extended in the literature such as [7,8,9,10]. Among them, Liu andLiu [7] presents the concept of credibility measure based on possibility distri-bution, Liu [8] develops credibility theory, and Liu and Liu [9] proposed an

Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part II, LNCS 6146, pp. 18, 2010.c Springer-Verlag Berlin Heidelberg 2010

2 Y. Liu and X. Zhang

axiomatic framework from which fuzzy possibility theory was developed. Cred-ibility theory provides the theoretical foundation for optimization under possi-bilistic uncertainty [11,12,13,14,15,16]. In addition, Gao [17] and Hua [18] dis-cussed the properties of covariance of fuzzy variables. The objective of this paperis also to study the correlations of fuzzy variables. Since the covariance of a pairfuzzy variables is dened by nonlinear fuzzy integral, its computation for gen-eral fuzzy variables is a challenge issue for research, and very often relies onapproximation scheme and intelligent computing. To avoid this diculty, weconsider the case when the joint possibility distribution of the fuzzy variables isthe minimum of its marginal possibility distributions, and derive several usefulcovariance formulas for common triangular and trapezoidal fuzzy variable. Theobtained results have potential applications in portfolio optimization problemswhen the correlations among fuzzy returns are considered.

Our paper proceeds as follows. In Section 2, we review several required fun-damental concepts. Under mild assumptions, Section 3 derives several usefulcovariance formulas for triangular fuzzy variables. An extension result abouttrapezoidal fuzzy variables is reported in Section 4. Section 5 concludes the pa-per and points out our future research in this eld.

2 Fuzzy Variables

Let be a fuzzy variable with a possibility distribution : [0, 1]. Then forany r , the possibility and credibility of an event { r} were dened by

Pos{ r} = suptr

(t), and Cr{ r} = 12 (1 + suptr (t) supt

On the Correlations between Fuzzy Variables 3

3 Correlations between Triangular Fuzzy Variables

Since the covariance of fuzzy variables is dened by nonlinear fuzzy integral,its computation for general fuzzy variables is a challenge issue for research,and usually relies on intelligent computing. In this section, if and are twofuzzy variables with possibility distributions and , respectively. In orderto compute their covariance, we assume that joint possibility distribution ,and marginal possibility distributions and have the following relation-ship: ,(s, t) = (s) (t) for any (s, t) 2. This property is called theindependence between and , and has been studied in [19].

In this section, we limit ourself to triangular fuzzy variables. In the case whenone of triangular fuzzy variables is symmetric, we have the following result:

Theorem 1. If = (r0 a, r0, r0 + a) and = (r0 b, r0, r0 + c) are triangularfuzzy variables such that is symmetric with a > 0, b > 0, and c > 0, then wehave Cov[, ] = 0.

Proof. Denote by = E[], and = E[]. Since E[] = r0, we have = E[] = (a, 0, a). Therefore, the -cut of is = [L , R ], whereL = a( 1), and R = a(1 ) for any 0 < 1.

On the other hand, according to

E[] =4r0 b + c

4, = E[] = (3b c

4,b c

4,b + 3c

4),

we know the -cut of is = [L ,

R ], where

L = (4b 3b c)/4, and

R = (b + 3c 4c)/4 for any 0 < 1.Using the notations above, we get the -cut of fuzzy variable as follows

() = [()inf(), ()sup()] = [()L, ()R ]

= [min{L L , L R , R L , R R },max{L L , L R , R L , R R }].Case I. If 0 < 1/2, then

L < 0, R > 0, |L | = R , L < 0, R > 0, |L | R .

Therefore, we have ()L = L R , and ()R = R R .Case II. If 1/2 < 1, then

L < 0, R > 0, |L | = R , L < 0, R > 0, |L | > R .

Thus, we have ()L = L L , and ()R = R L .Combining the above gives

()inf() = ()L ={

L R , if 0 < 12

L L , if

12 < 1,

and

()sup() = ()R ={

R R , if 0 < 12

R L , if

12 < 1.

Finally, it follows from (3) that Cov[, ] = 0, which completes the proof of thetheorem.

4 Y. Liu and X. Zhang

In the case when the left spreads are greater than the right spreads for bothtriangular fuzzy variables, we have:

Theorem 2. Let = (r0 a, r0, r0 + b) and = (r0 c, r0, r0 + d) be triangularfuzzy variables such that the left spreads of and are greater than theirrespective right spreads in the sense a > b > 0, and c > d > 0.

(i) If bc ad, a = c, and b = d, then

Cov[, ] = 132 (30ac+2bc+22ad+10bd

6 (3a+b)3(ac+ad)

12a3

+ (3a+b)2(7ad+7ac+bd+bc)

8a2 (3a+b)(bd+bc+3ad+3ac)a ).(ii) If bc < ad, then

Cov[, ] = 132 (30ac+2ad+22bc+10bd

6 (3c+d)3(ac+bc)

12c3

+ (3c+d)2(7bc+7ac+ad+bd)

8c2 (3c+d)(ad+bd+3ac+3bc)c ).Proof. We only prove assertion (i), and (ii) can be proved similarly.

If we denote = E[], and = E[], then we have

E[] =4r0 a + b

4, and = E[] = (3a b

4,a b

4,a + 3b

4).

By the possibility distribution of , we get the -cut of is = [L ,

R ],

where L = (4a 3a b)/4, and R = (a + 3b 4b)/4 for 0 < 1.On the other hand, from

E[] =4r0 c + d

4, and = E[] = (3c d

4,c d

4,c + 3d

4),

we get the -cut of is = [L , R ], where L = (4c 3c d)/4, andR = (c + 3d 4d)/4 for 0 < 1.

As a consequence, in this case, the -cut of can be represented as

() = [()inf(), ()sup()] = [()L, ()R ]

= [min{L L , L R , R L , R R },max{L L , L R , R L , R R }].By the supposition, bc ad, a = c, and b = d, we have

(3c + d)/4c (3a + b)/4a < (3b + a)/4b (3d + c)/4d.Case I. If 0 < 1/2, then

L < 0, R > 0, |L | R , and L < 0, R > 0, |L | R .

Therefore, one has ()L = min{L R , R L }, and ()R = L L .According to the following inequality

R L L R = a+3b4b4 4c3cd4 4a3ab4 c+3d4d4

= (ad bc)( 12 )( 1) < 0,we known ()L =

R

L .

On the Correlations between Fuzzy Variables 5

Case II. If 1/2 < < (3c + d)/4c, then

L < 0, R > 0, |L | < R , and L < 0, R > 0, |L | < R .

Therefore, we have ()L = min{L R , R L }, and ()R = R R .By the following inequality

R L L R = a+3b4b4 4c3cd4 4a3ab4 c+3d4d4

= (ad bc)( 12 )( 1) > 0,

we get ()L = L R .Case III. If = (3c + d)/4c, then

L < 0, R > 0, |L | < R , and L = 0, R > 0, L < R .

In this case, we have ()L = L

R , and (

)R = R

R .

Case IV. If (3c + d)/4c < (3a + b)/4a, thenL 0, R > 0, |L | < R , and L > 0, R > 0, L < R ,

which lead to ()L = L

R , and (

)R = R

R .

Combining the cases II, III and IV gives ()L = L R , and ()R =R

R whenever 1/2 < (3a + b)/4a.

Case V. If (3a + b)/4a < 1, then 0 < L < R , 0 < L < R . It followsthat ()L = L L , and ()R = R R .

Finally, from the above computational results, we have

()inf() = ()L =

R

L , if 0 < 12

L R , if

12 < 3a+b4a

L L , if

3a+b4a < 1,

and

()sup() = ()R =

L L , if 0 < 12R R , if

12 < 3a+b4a

R R , if3a+b4a < 1.

As a consequence, by (3), we have the desired result. The proof of assertion (i)is complete.

For triangular fuzzy variables, in the case when their right spreads are greaterthan their left spreads, we have:

Theorem 3. Let = (r0 a, r0, r0 + b) and = (r0 c, r0, r0 + d) be triangularfuzzy variables such that the right spreads of and are greater than theirrespective left spreads in the sense b > a > 0, d > c > 0.

(i) If ad bc , b = d, and a = c, then

Cov[, ] = 132 (30bd+2ad+22bc+10ac

6 (3b+a)3(bd+bc)

12b3

+ (3b+a)2(7bc+7bd+ac+ad)

8b2 (3b+a)(ac+ad+3bc+3bd)b ).

6 Y. Liu and X. Zhang

(ii) If ad < bc, then

Cov[, ] = 132 (30bd+2bc+22ad+10ac

6 (3d+c)3(ad+bd)

12d3

+ (3d+c)2(7ad+7bd+ac+bc)

8d2 (3d+c)(ac+bc+3bd+3ad)d ).The next theorem deals with the case when the left spread of one fuzzy variableis greater than its right spread, while the left spread of another fuzzy variable issmaller than its right spread.

Theorem 4. Let = (r0 a, r0, r0 + b) and = (r0 c, r0, r0 + d) be triangularfuzzy variables such that a > b > 0, and d > c > 0.

(i) If bd < ac, then

Cov[, ] = 132 ( 30ad+2ac+22bd+10bc6 + (c+3d)3(bd+ad)

12d3

(c+3d)2(7ad+7bd+bc+ac)8d2 + (c+3d)(bc+ac+3ad+3bd)d ).(ii) If bd ac, a = d, and b = c, then

Cov[, ] = 132 ( 30ad+2bd+22ac+10bc6 + (b+3a)3(ac+ad)

12a3

(b+3a)2(7ac+7ad+bc+bd)8a2 + (b+3a)(bc+bd+3ad+3ac)a ).

4 Correlations between Trapezoidal Fuzzy Variables

Due to the limitation of nonlinear fuzzy integrals, the computation about thecovariance of a pair general fuzzy variables is usually dicult. In this section,we give an extension result about the correlations between trapezoidal fuzzyvariables, which is summarized in the following theorem.

Theorem 5. Let = (r1 a, r1, r2, r2 + b) and = (r3 c, r3, r4, r4 + d) betrapezoidal fuzzy variables with a > 0, b > 0, c > 0, and d > 0.

(i) If L < R 0, L 0 < R , or L 0 < R , L 0 < R , andL

R <

R

L ,

L

L >

R

R , then Cov[, ] = (ac ad)/24.

(ii) If L 0 < R , L < R < 0, or L 0 < R , L 0 < R , andL

R >

R

L ,

L

L >

R

R , then Cov[, ] = (ac bc)/24.

(iii) If L 0 < R , 0 < L < R , or L 0 < R , L 0 < R , andL

R <

R

L ,

L

L <

R

R , then Cov[, ] = (bd ad)/24.

(iv) If 0 < L < R , L 0 < R , or L 0 < R , L 0 < R , andL

R >

R

L ,

L

L <

R

R , then Cov[, ] = (bd bc)/24.

(v) If L < R 0, L < R 0, or 0 < L < R , 0 < L < R , thenCov[, ] = 5ac + 5bd + 3ad + 3bc/48 + (c + d)(r2 r1)/8

+(a + b)(r4 r3)/8 + (r4 r3)(r2 r1)/4.(vi) If L <

R 0, 0 < L < R , or 0 < L < R , L < R 0, then

Cov[, ] = 5ad 5bc 3bd 3ac/48 + (a + b)(r3 r4)/8+(c + d)(r1 r2)/8 + (r2 r1)(r3 r4)/4.

On the Correlations between Fuzzy Variables 7

5 Conclusions and Future Research

The correlations between fuzzy variables is an important issue in fuzzy com-munity. Due to the limitation of nonlinear fuzzy integrals, the covariance canvery often only be obtained numerically for general fuzzy variables with knownpossibility distributions. In this paper, we focused on the computation of co-variance for triangular and trapezoidal fuzzy variables. Under the assumptionthat the joint possibility distribution is the minimum of its marginal possibilitydistributions, we derived several useful covariance formulas. The obtained re-sults have potential applications in portfolio optimization when we consider thecorrelations among fuzzy returns, which will be addressed in our future research.

Acknowledgments. This work was supported by the National Nature ScienceFoundation of China (NSFC) under Grant No. 60974134.

References

1. Chen, H., Chang, K., Cheng, L.: Estimation of Means and Covariances of Inverse-Gaussian Order Statistics. European Journal of Operational Research 155, 154169(2004)

2. Cuadras, C.M.: On the Covariance between Functions. Journal of MultivariateAnalysis 81, 1927 (2002)

3. Hirschberger, M., Qi, Y., Steuer, R.E.: Randomly Generating Portfolio Selec-tion Convariance Matrices with Specied Distributional Characteristics. EuropeanJournal of Operational Research 177, 16101625 (2007)

4. Koppelman, F., Sethi, V.: Incorporating Variance and Covariance Heterogeneityin the Generalized Nested Logit Model: an Application to Modeling Long DistanceTravel Choice Behavior. Transportation Research Part B 39, 825853 (2005)

5. Popescu, I.: Robust Mean Covariance Solutions for Stochastic Optimization. Op-erations Research 55, 98112 (2007)

6. Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets andSystems 1, 328 (1978)

7. Liu, B., Liu, Y.K.: Expected Value of Fuzzy Variable and Fuzzy Expected ValueModels. IEEE Transactions on Fuzzy Systems 10, 445450 (2002)

8. Liu, B.: Uncertainty Theory. Springer, Berlin (2004)9. Liu, Z., Liu, Y.: Type-2 Fuzzy Variables and Their Arithmetic. Soft Computing 14,

729747 (2010)10. Qin, R., Hao, F.: Computing the Mean Chance Distributions of Fuzzy Random

Variables. Journal of Uncertain Systems 2, 299312 (2008)11. Liu, Y.K.: The Convergent Results about Approximating Fuzzy Random Minimum

Risk Problems. Applied Mathematics and Computation 205, 608621 (2008)12. Liu, Y., Tian, M.: Convergence of Optimal Solutions about Approximation Scheme

for Fuzzy Programming with Minimum-Risk Criteria. Computers & Mathematicswith Applications 57, 867884 (2009)

13. Liu, Y., Liu, Z., Gao, J.: The Modes of Convergence in the Approximation of FuzzyRandom Optimization Problems. Soft Computing 13, 117125 (2009)

8 Y. Liu and X. Zhang

14. Lan, Y., Liu, Y., Sun, G.: Modeling Fuzzy Multi-Period Production Planning andSourcing Problem with Credibility Service Levels. Journal of Computational andApplied Mathematics 231, 208221 (2009)

15. Sun, G., Liu, Y., Lan, Y.: Optimizing Material Procurement Planning Problem byTwo-Stage Fuzzy Programming. Computers & Industrial Engineering 58, 97107(2010)

16. Qin, R., Liu, Y.: Modeling Data Envelopment Analysis by Chance Method inHybrid Uncertain Environments. Mathematics and Computers in Simulation 80,922950 (2010)

17. Gao, X.: Some Properties of Covariance of Fuzzy Variables. In: 3th Interna-tional Conference on Information and Management Sciences, vol. 3, pp. 304307.California Polytechnic State University, USA (2004)

18. Hua, N.: Properties of Moment and Covariance of Fuzzy Variables. Bachelor Thesis,Department of Mathematical Science, Tsinghua University (2003)

19. Liu, Y.K., Gao, J.: The Independence of Fuzzy Variables with Applications toFuzzy Random Optimization. International Journal of Uncertainty, Fuzziness &Knowledge-Based Systems 15, 120 (2007)

20. Liu, Y.K., Liu, B.: Expected Value Operator of Random Fuzzy Variable and Ran-dom Fuzzy Expected Value Models. International Journal of Uncertainty, Fuzziness& Knowledge-Based Systems 11, 195215 (2003)

Modeling Fuzzy Data Envelopment Analysiswith Expectation Criterion

Xiaodong Dai, Ying Liu, and Rui Qin

College of Mathematics & Computer Science, Hebei UniversityBaoding 071002, Hebei, China

daixiaodong@cmc.hbu.edu.cn, yingliu@hbu.edu.cn, qinrui07@163.com

Abstract. This paper presents a new class of fuzzy expectation data en-velopment analysis (FEDEA) models with credibility constraints. Sincethe proposed model contains the credibility of fuzzy events in the con-straints and the expected value of a fuzzy variable in the objective, thesolution process is very complex. Thus, in the case when the inputs andoutputs are mutually independent trapezoidal fuzzy variables, we dis-cuss the equivalent nonlinear forms of the programming model, whichcan be solved by standard optimization software. At the end of this pa-per, one numerical example is also provided to illustrate the eciency ofdecision-making unites (DMUs) in the proposed model.

Keywords: Data envelopment analysis, Credibility constraint, Fuzzyvariable, Expected value, Eciency.

1 Introduction

Data envelopment analysis (DEA) was initially proposed by Charnes, Cooperand Rhodes [1]. It is an evaluation method for measuring the relative eciencyof a set of homogeneous DMUs with multiple inputs and multiple outputs. Sincethe rst DEA model CCR [1], DEA has been studied by a number of researchersin many elds [2,3,4].

The advantage of the DEA method is that it does not require either a prioriweights or the explicit specication of functional relations between the multipleinputs and outputs. However, when evaluating the eciency, the data in tradi-tional DEA models must be crisp, and the eciency is very sensitive to datavariations. To deal with stochastic data variations, some researchers proposedseveral DEA models. For example, Cooper, Huang and Li [5] developed a sat-iscing DEA model with chance constrained programming; Olesen and Peterso[6] developed a probabilistic constrained DEA model. For more stochastic DEAapproaches, the interested readers may refer to [7,8,9].

On the other hand, to deal with fuzziness in the real world problems, Zadeh[10] proposed the concept of fuzzy set. Recently, the credibility theory [11], meanchance theory and fuzzy possibility theory [12] have also been proposed to treat

Corresponding author.

Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part II, LNCS 6146, pp. 916, 2010.c Springer-Verlag Berlin Heidelberg 2010

10 X. Dai, Y. Liu, and R. Qin

fuzzy phenomena existing in real-life problems. For more theories and applica-tions of credibility theory and mean chance theory, the interested readers mayrefer to [13,14,15,16]. In fuzzy environments, some researchers extended the tra-ditional DEA and proposed several fuzzy DEA models. For example, Entani,Maeda and Tanaka [17] developed a new pair of interval DEA models; Saen [18]proposed a new pair of assurance region-nondiscretionary factors-imprecise DEAmodels, and Triantis and Girod [19] proposed a mathematical programming ap-proach to transforming fuzzy input and output data into crisp data.

This paper attempts to establish a new class of fuzzy DEA models basedon credibility theory [11], and discuss its equivalent nonlinear forms when theinputs and outputs are mutually independent trapezoidal fuzzy variables. Therest of this paper is organized as follows. In Section 2, we present the fuzzyexpectation DEA models with fuzzy inputs and fuzzy outputs. Section 3 discussesthe equivalents of credibility constraints and the expectation objective in somespecial cases. In Section 4, we provide a numerical example to illustrate therelative eciency in the proposed model and the eectiveness of our solutionmethod. Section 5 draws our conclusions.

2 Fuzzy DEA Formulation

The traditional DEA model, which was proposed by Charnes, Cooper and Rhodes(CCR) [1], is built as

maxu,v

vT y0uTx0

subject to vT yi

uTxi 1, i = 1, , n

u 0, u = 0v 0, v = 0,

(1)

where xi represent the input column vector of DMUi, x0 represents the inputcolumn vector of DMU0; yi represent the output column vector of DMUi, y0represents the output column vector of DMU0; u m and v s are theweights of the input and output column vectors.

Model (1) is used to evaluate the relative eciency of DMUs with crisp in-puts and outputs. However, in many cases, we can only obtain the possibilitydistributions of the inputs and outputs. Thus in this paper, we assume that theinputs and outputs are characterized by fuzzy variables with known possibilitydistributions. Based on fuzzy expected value operator and credibility measure[20], we can establish the following fuzzy expectation DEA model

maxu,v

VEDEA = E[vT 0uT 0

]subject to Cr{uT i vT i 0} i, i = 1, 2, , n

u 0, u = 0v 0, v = 0,

(2)

where the notations are illustrated in Table 1.

Modeling Fuzzy Data Envelopment Analysis with Expectation Criterion 11

Table 1. List of Notations for Model (2)

Notations Denitions

0 the fuzzy input column vector consumed by DMU0i the fuzzy input column vector consumed by DMUi, i = 1, , n0 the fuzzy output column vector produced by DMU0i the fuzzy output column vector produced by DMUi, i = 1, , nu m the weights of the fuzzy input column vectorv s the weights of the fuzzy output column vectori (0, 1] the predetermined credibility level corresponding to the ith constraint

In model (2), our purpose is to seek a decision (u, v) with the maximum valueof E

[vT 0/u

T 0], while the fuzzy event {uT i vT i 0} is satised at least

with credibility level i. Thus, we adopt the concept of expectation ecientvalue to illustrate the eciency of DMU0. The optimal value of model (2) isreferred to as the expectation ecient value of DMU0, and the bigger the valueis, the more ecient it is.

Model (2) is very dicult to solve. Therefore, in the next section, we willdiscuss the equivalent forms of model (2) in some special cases.

3 Deterministic Equivalent Programming of Model (2)

In the following, we rst handle the constraint functions.

3.1 Handing Credibility Constraints

When the inputs and outputs are mutually independent trapezoidal fuzzy vec-tors, the constraints of model (2) can be transformed to their equivalent linearforms according to the following theorem.

Theorem 1. Let i = (Xiai, Xi, Xi+bi, Xi+ci), i = (Yiai, Yi, Yi+bi, Yi+ci)be independent trapezoidal fuzzy vectors with ai, bi, ci, ai, bi, ci positive numbers.Then Cr{uT i vT i 0} i in the model (2) is equivalent to

gi(u, v) 0, (3)

where gi(u, v) = uT (Xi (2i 1)ai) vT (Yi + (2i 1)ci + 2(1 i)bi).Proof. It is obvious that uT i vT i = (uT (Xi ai) vT (Yi + ci), uTXi vT (Yi + bi), uT (Xi + bi) vTYi, uT (Xi + ci) vT (Yi ai)). When 0.5 < i < 1(i = 1, , n), according to the distributions of uT i vT i and the denitionof the credibility measure, we have

uT (Xi ai) vT (Yi + ci) < 0 < uTXi vT (Yi + bi).

12 X. Dai, Y. Liu, and R. Qin

Thus, Cr{uT i vT i 0} i is equivalent touT (Xi (2i 1)ai) vT (Yi + (2i 1)ci + 2(1 i)bi) 0.

The proof of the theorem is complete.

By the transformation process proposed above, we have turned the constraintfunctions of model (2) to their equivalent linear forms. In the following, we willdiscuss the equivalent form of the objective.

3.2 Equivalent Representation of the Expectation Objective

In this section, we rst deduce some formulas for the expected value of thequotient of two independent fuzzy variables.

Theorem 2. Suppose = (Xa,X,X+b,X+c) and = (Y a, Y, Y +b, Y +c)are two mutually independent trapezoidal fuzzy variables, where a, b, c, a, b, c arepositive numbers, b < c, b < c and X > a or X < c. Then we have

E[

]= a2(cb) + bc2a + 12a

(Y + b + cba X

)ln XXa

+ 12(cb)(Y + acb(X + b)

)lnX+cX+b .

(4)

Proof. We only prove the case X > a, and when X < c, the proof is similar.When X > a, is a positive fuzzy variable. Thus, we have

E[

]= +0 Cr

{ r

}dr 0Cr{ r} dr

= +0 Cr{ r 0}dr

0Cr{ r 0}dr.

(5)

Since r = (Y rX (rc+ a), Y rX rb, Y rX + b, Y rx+ (c+ ra)),according to credibility measure of a fuzzy event, we have

Cr{ r 0} =

1, if r < YaX+c12 +

Yr(X+b)2(a+r(cb)) , if

YaX+c r < YX+b

12 , if

YX+b r < Y +bX

12 +

YrX+b2(ra+cb) , if

Y +bX r < Y +cXa

0, if r Y +cXa ,

Cr{ r 0} =

0, if r < YaX+c12 Yr(X+b)2(a+r(cb)) , if YaX+c r < YX+b12 , if

YX+b r < Y +bX

12 YrX+b2(ra+cb) , if Y +bX r < Y +cXa1, if r Y +cXa .

In the following, we calculate E[/] according to ve cases.(i) If (Y a)/(X + c) > 0, i.e. Y > a, then (5) becomes to

E[

]= Ya

X+c0 1dr +

YX+bYaX+c

(12 +

Yr(X+b)2(a+r(cb))

)dr +

Y+bXY

X+b

12dr

+ Y+c

XaY+bX

(12 +

YrX+b2(ra+cb)

)dr = YaX+c + M1 +

12 (

Y +bX YX+b ) + M2,

Modeling Fuzzy Data Envelopment Analysis with Expectation Criterion 13

where

M1 = 12(

YX+b YaX+c

)+ Y

X+bYaX+c

( X+b2(cb) + 12(cb)

acb (X+b)+Y

acb+r

)dr

=(

12 X+b2(cb)

)(Y

X+b YaX+c)+ 12(cb)

(a

cb (X + b) + Y)ln X+cX+b ,

M2 =( 12 X2a

) (Y +cXa Y +bX

)+ 12a

(cba X + Y + b

)ln XXa .

Therefore, formula (4) is valid for this case.(ii) If (Y a)/(X + c) 0 < Y/(X + b), i.e. 0 < Y a, then (5) becomes to

E[

]= Y

X+b0

(12 +

Yr(X+b)2(a+r(cb))

)dr +

Y+bXY

X+b

12dr +

Y+cXaY+bX

(12 +

YrX+b2(ra+cb)

)dr

0YaX+c

(12 Yr(X+b)2(a+r(cb))

)dr = M1 + 12 (

Y +bX YX+b ) + M2 M3,

where M2 is the same with the M2 in Case (i), and

M1 =(

12 X+b2(cb)

)Y

X+b +1

2(cb)(

acb (X + b) + Y

)ln a(X+b)+Y (cb)a(X+b) ,

M3=(

X+b2(cb) 12

)(Y

X+b YaX+c) 12(cb)

(a

cb (X + b) + Y)ln a(X+c)a(X+b)+Y (cb) ,

Therefore, formula (4) is valid for this case.(iii) If Y/(X + b) 0 < (Y + b)/X , i.e. b < Y 0, then (5) becomes to

E[

]= Y+b

X

012dr +

Y+cXaY+bX

(12 +

YrX+b2(ra+cb)

)dr YX+bYa

X+c

(12 Yr(X+b)2(a+r(cb))

)dr

0YX+b

12dr =

Y +b2X + M2 M3 + Y2(X+b) ,

where M2 is the same with the M2 in Case (i), and

M3 = X+c2(cb)(

YX+b YaX+c

) 12(cb)

(a

cb (X + b) + Y)ln X+cX+b ,

Therefore, formula (4) is valid for this case.(iv) If (Y + b)/X 0 < (Y + c)/(X a), i.e., c < Y b, then (5) becomesto

E[

]= Y+c

Xa0

(12 +

YrX+b2(ra+cb)

)dr YX+bYa

X+c

(12 Yr(X+b)2(a+r(cb))

)dr Y+bXY

X+b

12dr

0Y+bX

(12 YrX+b2(ra+cb)

)dr = M2 M3 12

(Y +bX Y2(X+b)

)M4,

where M3 is the same with the M3 in Case (iii), and

M2 =( 12 X2a

)Y +cXa +

12a

(cba X + Y + b

)ln X(cb)+a(Y +a)Xa ,

M4 = (12 +

X2a

)Y +bX 12a

(cba X + Y + b

)ln X

X(cb)+a(Y +a) .

Therefore, formula (4) is valid for this case.(v) If (Y + c)/(X a) 0, i.e. Y c, then (5) becomes to

E[

]= YX+bYa

X+c

(12 Yr(X+b)2(a+r(cb))

)dr Y+bXY

X+b

12dr

Y+cXaY+bX

(12 YrX+b2(ra+cb)

)dr

0Y+cXa

1dr = M2 12(

Y +bX Y2(X+b)

)M3 + Y +cXa ,

14 X. Dai, Y. Liu, and R. Qin

where M3 is the same with the M3 in Case (iii), and

M2 = X+c2(cb)(

YX+b YaX+c

) 12(cb)

(a

cb (X + b) + Y)ln X+cX+b .

Therefore, formula (4) is valid for this case. The proof of the theorem is complete.

3.3 Deterministic Equivalent Programming

Denote the inputs and outputs of DMU0 as 0 = (1,0, , m,0)T and 0 =(1,0, , s,0)T . Suppose that j,0 = (Xj,0 aj,0, Xj,0, Xj,0 + bj,0, Xj,0 + cj,0)and k,0 = (Yk,0 ak,0, Yk,0, Yk,0 + bk,0, Yk,0 + ck,0) are mutually independenttrapezoidal fuzzy variables, where aj,0, bj,0, ck,0, aj,0, bj,0, ck,0 are positive num-bers, and Xj,0 > aj,0, Yk,0 > ak,0 for j = 1, ,m, k = 1, , s. Then accordingto Theorem 2, we have

f0(u, v) = E[vT 0uT 0

]= a2(cb) + bc2a + 12a

(Y + b + cba X

)ln XXa

+ 12(cb)(Y + acb (X + b)

)lnX+cX+b ,

(6)

where

a =m

j=1 ujaj,0, b =m

j=1 ujbj,0, c =s

k=1 vkck,0, a =s

k=1 vk ak,0,

b =s

k=1 vk bk,0, c =s

k=1 vk ck,0, X =m

j=1 ujXj,0, Y =s

k=1 vkYk,0.

As a consequence, when the inputs and outputs are mutually independent trape-zoidal fuzzy variables, the model (2) can be transformed into the following equiv-alent nonlinear programming

maxu,v

f0(u, v)

subject to gi(u, v) 0, i = 1, 2, , nu 0, u = 0v 0, v = 0,

(7)

where f0(u, v) and gi(u, v) are dened by (6) and (3), respectively.The model (7) is a nonlinear problem with linear constraints, which can be

solved by standard optimization solvers.

4 Numerical Example

In order to illustrate the solution method for the proposed FDEA, we providea numerical example with ve DMUs, and each DMU has four fuzzy inputsand four fuzzy outputs. In addition, for each DMU, the inputs and outputs arecharacterized by mutually independent trapezoidal fuzzy variables, as shown inTable 2. For simplicity, we assume that 1 = 2 = = 5 = .

With model (7), we obtain the results of evaluating all the DMUs with cred-ibility level = 0.95 with Lingo software [21], as shown in Table 3. From the

Modeling Fuzzy Data Envelopment Analysis with Expectation Criterion 15

Table 2. Four Fuzzy Inputs and Outputs for Five DMUs

DMUi Input 1 Input 2 Input 3 Input 4i=1 (2.8, 3.0, 3.1, 3.4) (2.0, 2.1, 2.3, 2.4) (2.5, 2.7, 2.9, 3.0) (3.6, 3.9, 4.1, 4.2)i=2 (1.8, 1.9, 2.0, 2.2) (1.4, 1.6, 1,7, 1.8) (2.2, 2.3, 2.4, 2.5) (3.1, 3.2, 3.4, 3.7)i=3 (2.5, 2.6, 2.8, 2.9) (1.8, 2.0, 2.4, 2.5) (2.0, 2.5, 2.8, 3.0) (4.1, 4.2, 4.4, 4.5)i=4 (3.0, 3.1, 3.3, 3.5) (4.1, 4.3, 4.5, 4.6) (3.8, 3.9, 4.0, 4.1) (4.6, 4.8, 4.9, 5.0)i=5 (4.8, 4.9, 5.0, 5.3) (6.1, 6.2, 6.4, 6.6) (4.4, 4.5, 4.8, 5.0) (5.2, 5.5, 5.6, 5.8)

DMUi Output 1 Output 2 Output 3 Output 4i=1 (4.0, 4.1, 4.2, 4.4) (3.0, 3.2, 3.4, 3.5) (3.6, 3.8, 4.1, 4.2) (4.8, 4.9, 5.0, 5.1)i=2 (3.4, 3.8, 4.0, 4.2) (4.0, 4.3, 4.5, 4.6) (3.5, 3.6, 3.7, 3.9) (4.0, 4.1, 4.3, 4.4)i=3 (4.5, 4.8, 5.0, 5.5) (3.8, 3.9, 4.0, 4.1) (3.0, 3.1, 3.3, 3.4) (4.3, 4.5, 4.6, 4.7)i=4 (4.8, 5.0, 5.1, 5.4) (4.3, 4.4, 4.5, 4.7) (5.2, 5.3, 5.4, 5.5) (6.0, 6.2, 6.4, 6.8)i=5 (5.8, 6.0, 6.3, 6.4) (6.5, 6.7, 6.8, 6.9) (4.9, 5.0, 5.2, 5.4) (5.9, 6.3, 6.5, 6.8)

Table 3. Results of evaluation with =0.95 in model (1)

DMUs Optimal solution (u,v) Eciency valueDMU1 (0.0000,0.0000,0.5685,1.0000,0.0000,0.0000,0.0000,0.9946) 0.8946490DMU2 (0.5397,0.0000,1.0000,0.0000,0.0000,0.0000,0.0000,0.7259) 0.8965842DMU3 (0.0000,0.0000,0.0663,1.0000,0.7791,0.0000,0.0000,0.0000) 0.8660948DMU4 (0.0000,0.0000,0.0000,1.0000,0.0000,0.0000,0.3486,0.4003) 0.9149018DMU5 (0.0000,0.0000,0.0000,1.0000,0.7440,0.0000,0.0000,0.0000) 0.8268326

results, we know that DMU4 is the most ecient with expectation ecient value0.9149018, followed by DMU2 and DMU1, which implies that DMU4 has thebest position in competition. If the DMUs with less expectation ecient valueswant to improve their position in competition, they should decrease their inputs.Therefore, with the expectation ecient values, the decision makers can obtainmore information and thus make better decisions in competition.

5 Conclusions

This paper proposed a new class of fuzzy DEA models with credibility constraintsand expectation objective. In order to solve the proposed model, for trapezoidalfuzzy inputs and outputs, we discussed the equivalent representation for theconstraints and the objective. With such transformations, the proposed DEAmodel can be turned into its equivalent nonlinear programming, which can besolved by standard optimization softwares. At last, a numerical example wasprovided to illustrate the eciency of DMUs in the proposed DEA model.

Acknowledgments. This work was supported by the National Nature ScienceFoundation of China (NSFC) under Grant No. 60974134.

16 X. Dai, Y. Liu, and R. Qin

References

1. Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the Eciency of DecisionMaking Units. European Journal of Operational Research 2, 429444 (1978)

2. Cook, W.D., Seiford, L.M.: Data Envelopment Analysis (DEA)-Thirty Years on.European Journal of Operational Research 192, 117 (2009)

3. Cooper, W.W., Seiford, L.M., Tone, K.: Data Envelopment Analysis. SpringerScience and Business Media, New York (2007)

4. Emrouznejad, A., Parker, B.R., Tavares, G.: Evaluation of Research in Eciencyand Productivity: A Survey and Analysis of the First 30 Years of Scholarly Liter-ature in DEA. Socio-Economic Planning Sciences 42, 151157 (2008)

5. Cooper, W.W., Huang, Z.M., Li, S.X.: Satiscing DEA Models under Chance Con-straints. Annals of Operations Research 66, 279295 (1996)

6. Olesen, O.B., Peterso, N.C.: Chance Constrained Eciency Evaluation. Manage-ment Science 41, 442457 (1995)

7. Desai, A., Ratick, S.J., Schinnar, A.P.: Data Envelopment Analysis with StochasticVariations in Data. Socio-Economic Planning Sciences 3, 147164 (2005)

8. Gong, L., Sun, B.: Eciency Measurement of Production Operations under Un-certainty. International Journal of Production Economics 39, 5566 (1995)

9. Retzla-Roberts, D.L., Morey, R.C.: A Goal Programming Method of Stochas-tic Allocative Data Envelopment Analysis. European Journal of OperationalResearch 71, 379397 (1993)

10. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338353 (1965)11. Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations.

Springer, Berlin (2004)12. Liu, Z.Q., Liu, Y.K.: Type-2 Fuzzy Variables and their Arithmetic. Soft

Computing 14(7), 729747 (2010)13. Lan, Y., Liu, Y.K., Sun, G.: Modeling Fuzzy Multi-period Production Planning

and Sourcing Problem with Credibility Service Levels. Journal of Computationaland Applied Mathematics 231, 208221 (2009)

14. Qin, R., Hao, F.F.: Computing the Mean Chance Distributions of Fuzzy RandomVariables. Journal of Uncertain Systems 2, 299312 (2008)

15. Qin, R., Liu, Y.K.: A New Data Envelopment Analysis Model with Fuzzy Ran-dom Inputs and Outputs. Journal of Applied Mathematics and Computing (2009),doi:10.1007/s12190-009-0289-7

16. Qin, R., Liu, Y.K.: Modeling Data Envelopment Analysis by Chance Method inHybrid Uncertain Environments. Mathematics and Computers in Simulation 80,922950 (2010)

17. Entani, T., Maeda, Y., Tanaka, H.: Dual Models of Interval DEA and its Extensionto Interval Data. European Journal of Operational Research 136, 3245 (2002)

18. Saen, R.F.: Technology Selection in the Presence of Imprecise Data, Weight Re-strictions, and Nondiscretionary Factors. The International Journal of AdvancedManufacturing Technology 41, 827838 (2009)

19. Triantis, K., Girod, O.: A Mathematical Programming Approach for MeasuringTechnical Eciency in a Fuzzy Environment. Journal of Productivity Analysis 10,85102 (1998)

20. Liu, B., Liu, Y.K.: Expected Value of Fuzzy Variable and Fuzzy Expected ValueModels. IEEE Transaction on Fuzzy Systems 10, 445450 (2002)

21. Mahmoud, M.E.: Appendix II: Lingo Software. Process Systems Engineering 7,389394 (2006)

Finding and Evaluating Fuzzy Clusters inNetworks

Jian Liu

LMAM and School of Mathematical Sciences, Peking University,Beijing 100871, P.R. China

dugujian@pku.edu.cn

Abstract. Fuzzy cluster validity criterion tends to evaluate the qualityof fuzzy partitions produced by fuzzy clustering algorithms. In this pa-per, an eective validity index for network fuzzy clustering is proposed,which involves the compactness and separation measures for each cluster.The simulated annealing strategy is used to minimize this validity index,associating with a dissimilarity-index-based fuzzy c-means iterative pro-cedure, under the framework of a random walker Markovian dynamicson the network. The proposed algorithm (SADIF) can eciently identifythe probabilities of each node belonging to dierent clusters during thecooling process. An appropriate number of clusters can be automaticallydetermined without any prior knowledge about the network structure.The computational results on several articial and real-world networksconrm the capability of the algorithm.

Keywords: Fuzzy clustering, Validity index, Dissimilarity index, Fuzzyc-means, Simulated annealing.

1 Introduction

Recently, the structure and dynamics of networks have been frequently concernedin physics and other elds as a foundation for the mathematical representation ofvarious complex systems [1,2,3]. Network models have also become popular toolsin social science, economics, the design of transportation and communicationsystems, banking systems, etc, due to our increased capability of analyzing thesemodels [4,5]. Modular organization of networks, closely related to the ideas ofgraph partitioning, has attracted considerable attention, and many real-worldnetworks appear to be organized into clusters that are densely connected withinthemselves but sparsely connected with the rest of the networks. A huge varietyof cluster detection techniques have been developed into partitioning the networkinto a small number of clusters [6,7,8,9,10,11], which are based variously oncentrality measures, ow models, random walks, optimization and many otherapproaches. On a related but dierent front, recent advances in computer visionand data mining have also relied heavily on the idea of viewing a data set oran image as a graph or a network, in order to extract information about theimportant features of the images or more generally, the data sets [12,13].

Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part II, LNCS 6146, pp. 1726, 2010.c Springer-Verlag Berlin Heidelberg 2010

18 J. Liu

The dissimilarity index for each pair of nodes and the corresponding hierar-chical algorithm to partition the networks are proposed in [9]. The basic idea isto associate the network with the random walker Markovian dynamics [14]. Intraditional clustering literature, a function called validity index [15] is often usedto evaluate the quality of clustering results, which has smaller values indicatingstronger cluster structure. This can motivate us to solve the fuzzy clusteringproblem by an analogy to the fuzzy c-means algorithm [16] and construct anextended formulation of Xie-Beni index under this measure. Then simulated an-nealing strategy [17,18] is utilized to obtain the minimum value of such index,associating with a dissimilarity-index-based fuzzy c-means iterative procedure.The fuzzy clustering contains more detailed information and has more predictivepower than the old way of doing network partition.

We will construct our algorithm simulated annealing with a dissimilarity-index-based fuzzy c-means (SADIF) for fuzzy partition of networks. From thenumerical performance to three model problems: the ad hoc network with 128nodes, the karate club network and and sample network generated from Gaussianmixture model, we can see that our algorithm can eciently and automaticallydetermine the optimal number of clusters and identify the probabilities of eachnode belonging to dierent clusters during the cooling process.

The rest of the paper is organized as follows. In Section 2, we briey introducethe dissimilarity index [9] which signies to what extent two nodes would like tobe in the same cluster, then proposed the extended fuzzy c-means and val