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Applied Soft Computing 12 (2012) 700–711

Contents lists available at SciVerse ScienceDirect

Applied Soft Computing

j ourna l ho me p age: www.elsev ier .com/ l ocate /asoc

eveloping a hybrid artificial intelligence model for outpatient visits forecastingn hospitals

smaeil Hadavandia, Hassan Shavandib, Arash Ghanbari c,∗, Salman Abbasian-Naghnehd

Department of Industrial Engineering, Amirkabir University of Technology, P.O. Box 15875-4413 Tehran, IranDepartment of Industrial Engineering, Sharif University of Technology, P.O. Box 11365-9466, Tehran, IranDepartment of Industrial Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, IranDepartment of Mathematics, Islamic Azad University Najafabad Branch, Najafabad, Iran

r t i c l e i n f o

rticle history:eceived 13 August 2010eceived in revised form 11 June 2011ccepted 1 September 2011vailable online 18 November 2011

eywords:

a b s t r a c t

Accurate forecasting of outpatient visits aids in decision-making and planning for the future and is thefoundation for greater and better utilization of resources and increased levels of outpatient care. It pro-vides the ability to better manage the ways in which outpatient’s needs and aspirations are planned anddelivered. This study presents a hybrid artificial intelligence (AI) model to develop a Mamdani type fuzzyrule based system to forecast outpatient visits with high accuracy. The hybrid model uses genetic algo-rithm for evolving knowledge base of fuzzy system. Actually it extracts useful patterns of information

enetic fuzzy systemata clusteringelf organizing mapumber of outpatient visitsorecasting

with a descriptive rule induction approach based on Genetic Fuzzy Systems (GFS). This is the first studyon using a GFS to constructing an expert system for outpatient visits forecasting problems. Evaluation ofthe proposed approach will be carried out by applying it for forecasting outpatient visits of the depart-ment of internal medicine in a hospital in Taiwan and four big hospitals in Iran. Results show that theproposed approach has high accuracy in comparison with other related studies in the literature, so it canbe considered as a suitable tool for outpatient visits forecasting problems.

. Introduction and literature review

Forecasting is the process of making projections about futureerformance based on existing historic data. The outpatient depart-ent in a hospital which provides patient diagnoses, treatment

nd health protection, is an important part of its organization andorecast outpatient visits is absolutely necessary in order to man-ge the hospital [1]. An accurate outpatient visits forecast aids inecision-making and planning for the future and is the founda-ion for greater and better utilization of resources and increasedevels of outpatient care. The accurate forecast of outpatient visitselps to have an appropriate planning for resources. For examplehe outpatient department can do a better scheduling for nursesnd doctors needed to care the patients. The outpatient depart-ent can also do a better planning for materials and drugs needed

n a considered period based on its outpatient visits forecasting.

n general the outpatient visits forecasting system can play as aecision support system for management and can increase theapabilities to improve the performance of department and resultn more patients satisfaction as well as more productivity. The gen-ral benefits and capabilities that the outpatient visits forecasting

∗ Corresponding author.E-mail addresses: es.hadavandi@gmail.com (E. Hadavandi),

rashghanbari@yahoo.com, arghanbari@ut.ac.ir (A. Ghanbari).

568-4946/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2011.09.018

© 2011 Elsevier B.V. All rights reserved.

system constructs for a hospital are: improved outpatient service,more effective employment of assets, improvement in outpatientthroughput, more effective operational planning, reduced costs andincreased revenues, more effective staff management and createsa proactive working environment.

Knowing the number of outpatient visits can help the expert ofhealth care administration make a strategic decision. Goldman et al.[2] denoted that the main factors behind the cost reduction were adecrease in the number of outpatient sessions per user, a decreasein inpatient admissions, a decrease in length-of-stay, and a decreasein costs per day. Further, we can get other valuable data by using thenumber of outpatient visits, for example, the revisiting outpatientratio is the number of revisiting outpatient divided by the numberof outpatient visits. If we could forecast the number more exactly,it would help the expert of health care administration effectivelymanage operation, distribute resource, and so on [1].

Some researchers have focused on outpatient visits forecastingwith high accuracy. They have presented classical and fuzzy timeseries methods for the problem of outpatient visits forecasting.Abdel-Aal and Mangoud [3] used two univariate time-seriesanalysis methods to model and forecast the monthly patient

volume at a primary healthcare clinic. Cheng et al. [1] proposeda new fuzzy time series method, which is based on weighted-transitional matrix, also proposed two new forecasting methods:the Expectation Method and the Grade-Selection Method for

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utpatient visits forecasting. They found the proposed methodsxhibit a relatively lower error rate in comparison to other fuzzyime series methods in literature such as methods proposedy Chen [4] and Yu [5], and could be more stable in facing thever-changing future trends.

Classical methods of forecasting are regression and time seriesodels. These models use piecewise linear function as basic ele-ents of prediction model. The functional form of the problem has

o be specified by the user. It could take a lot of time to experi-ent with the different possible functions and algorithms to obtain

he proper model. Also relationship between target variable andnfluencing factors in many time series is nonlinear and complex.t is hard or even impossible to have a precise mathematical modelescribing these relationships. These models also need the largemount of historical data in order to yield accurate results. There-ore, forecasting methods are needed today that are efficient underncomplete data conditions.

Nowadays, Artificial Intelligence techniques such as artificialeural networks (ANNs), fuzzy logic, and genetic algorithms (GAs)re popular research subjects, since they can deal with complexroblems in forecasting and other fields, which are difficult to solvey classical methods [6]. These techniques have been successfullysed in the place of forecasting problems [7–11]. A number oftudies have compared the capability of AI techniques with con-entional techniques such as ARIMA and Regression in the field oforecasting and they have found that AI-based systems have moreccurate results than conventional approaches such as ARIMA andegression [12–14].

An approach to increase the performance of AI-based techniquesnd enrich them to model and analyze the complex real worldroblems is to integrate the use of AI techniques and constructybrid models. Using hybrid models or combining several modelsas become a common practice to improve forecasting accuracynd the literature on this topic has expanded dramatically [15].

Among intelligent models, fuzzy rule based systems and arti-cial neural network (ANN) models are popular techniques for

orecasting time series in the recent decade. Despite the advan-ages of ANNs, they have weaknesses, one of the most importantf which is their requirement for large amounts of data in ordero yield accurate results. Also the training procedure of an ANN

odel is time consuming. Fuzzy forecasting methods are suitablender incomplete data conditions and require fewer observationshan other forecasting models do. Fuzzy logic offers a better wayo represent complicated situations in terms of simple natural lan-uage and has been applied very practically in many fields wherelassical models are difficult to implement for the design and learn-ng. However as the system complexity and nonlinearity increases,btaining a reliable and accurate knowledge base fuzzy systemsed to describe the system behavior become difficult. In this moreomplex environment hybridizing fuzzy logic systems and otherntelligent models can be very promising. One of the most popu-ar approaches is the hybridization between fuzzy logic and GAseading to Genetic Fuzzy Systems (GFSs) [16]. A GFS is basically

fuzzy system augmented by a learning process based on evolu-ionary computation, which includes genetic algorithms and othervolutionary algorithms (EAs) [17]. In recent years some articlesave been published in the favor of using GFS in behavior modelingrea and forecasting [14,18–20]. They have all obtained satisfac-ory results and concluded that using GFSs is very promising forhis area. Also a number of studies have compared the capability ofNNs and fuzzy systems in the field of forecasting and they have

ound that fuzzy systems have more accurate results than ANNs and

lassical time series models in complex and nonlinear environmentnd in case of limited data [12,14,21].

In time series forecasting, input data preprocessing maympact forecasting performance [22]. One of the popular data

mputing 12 (2012) 700–711 701

preprocessing stages is data clustering that is used in differentstudies to divide the data into sub-populations and reduce the com-plexity of the whole data space to something more homogeneousand reduce effects of noisy data [23,24], all of them have reportedthat using data clustering algorithm improves forecasting accuracy.

We take these clues to its extreme conclusion and present ahybrid artificial intelligence model to develop a Mamdani typefuzzy rule based system to forecast monthly outpatient visitsof hospitals. The hybrid model uses data clustering to improveforecasting accuracy and uses genetic algorithm for evolvingknowledge base of fuzzy system. The evaluation process is car-ried out by means of outpatient visits of the department of internalmedicine in five cases: a hospital in Taiwan with the same data setused by Cheng et al. [1] and four big hospitals in Iran.

2. Clustering-Based Genetic Fuzzy System (CGFS)

In this section we present a hybrid artificial intelligence modelcalled Clustering-Based Genetic Fuzzy System (CGFS) for construct-ing an expert system to deal with outpatient visits forecastingproblems. CGFS is composed of three main stages. At the first stagewe use Self-Organizing Map (SOM) neural network to cluster ourraw data into sub-populations and reduce the complexity of thewhole data space to something more homogeneous. In the secondstage, data in different clusters (divided by SOM technique) will befed into independent genetic fuzzy systems. At the last stage, weforecast outpatient visits by using constructed GFSs.

The framework of CGFS is shown in Fig. 1, and the details of eachstage are described below.

2.1. Data clustering by Self-Organizing Map (SOM) neuralnetwork

Clustering algorithms are classified to two groups: the agglom-erative hierarchical algorithms [25] such as the centroid and Wardmethods, and the nonhierarchical clustering [26], such as K-meansand SOM neural networks. Each of these algorithms has their ownadvantages and disadvantages. Depending on the application, aparticular type of clustering method should be chosen. Among clus-tering algorithms, because of the stable and flexible architecture ofSOM neural networks, it has been used in a wide range of appli-cations. Mangiameli et al. [27] made a comparison between theself-organizing map neural network clustering and the hierarchi-cal clustering methods. A large number of data sets were used totest the performance of SOM and the hierarchical clustering meth-ods. This research showed that SOM outperforms the hierarchicalmethods in clustering messy data and has better accuracy androbustness. There are also some researches in the field of forecast-ing which have used SOM neural networks for clustering data andthey have obtained good results [28,29]. So, in this paper we useSOM neural networks for clustering datasets.

Self-Organizing Map is an unsupervised learning algorithm. Thismethod was developed by Kohonen [30]. The SOM network con-sists of M neurons arranged in a 2-D rectangular or hexagonal grid.Each neuron i is assigned a weight vector, wi ∈ Rn (index i = (p, q)for 2-D map). At each training step t, a training data xt ∈ Rn is ran-domly drawn from data set and calculates the Euclidean distancesbetween xt and all neurons. A winning neuron with weight of wjcan be found according to the minimum distance to xt:

j = arg mini

||xt − wti ||, i ∈ {1, 2, . . . , M} (1)

Then, the SOM adjusts the weight of the winner neuron and

neighborhood neurons and moves closer to the input spaceaccording to:

wt+1t = wt

i + ˛t × htji × [xt − wt

i ] (2)

702 E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711

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here rj and ri are the position of winner neuron and neighbor-

ood neuron on map. �t is kernel width and decreasing with time.his process of weight-updating will be performed for a specifiedumber of iterations. The Statistica 7.0 software was used forpplying SOM clustering in this research.

f proposed CGFS.

2.2. Developing the genetic fuzzy system

Nowadays, fuzzy rule-based systems have been successfullyapplied to a wide range of real-world problems from different areas.In order to design an intelligent system of this kind for a concreteapplication, several tasks have to be performed. One of the mostimportant and difficult ones is to derive an appropriate knowledgebase (KB) about the problem. The KB stores the available knowledgein the form of fuzzy linguistic IF–THEN rules. It is composed of therule base (RB), constituted by the collection of rules in their sym-bolic forms, and the data base (DB), which contains the linguisticterm sets and the membership functions defining their meanings[31].

The difficulty presented by human experts to express their

knowledge in the form of fuzzy rules has made researchers developautomatic techniques to perform this task. In this sense, a largeamount of methods has been proposed to automatically generatefuzzy rules from numerical data. Usually, they use complex rule

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E. Hadavandi et al. / Applied S

eneration mechanisms such as neural networks [32] or geneticlgorithms [16].

GAs have been demonstrated to be a powerful tool for automat-ng the definition of the KB, since adaptive control, learning, andelf-organization may be considered in a lot of cases as optimiza-ion or search processes. In particular, the application to the design,earning, and tuning of KBs has produced quite promising results.hese approaches can be given the general name of genetic fuzzyystems [33].

In this paper we use a Mamdani-type fuzzy rule-based systemFRBS) for forecasting outpatient visits. In a Mamdani-type FRBS aommon rule represented as follows:

If X1 is A1 and X2 is A2 THEN Y is C1, where X1, X2 and Y areinguistic variables and A1, A2 and C1 are corresponding fuzzy sets.n the following we will describe evolutionary process that we usen this paper for evolving knowledge base of FRBS.

.2.1. Proposed Genetic Fuzzy System (GFS)In this section, we describe a novel Pittsburgh-style genetic

uzzy rule based system proposed by Carse et al. [34] which isharacterized by a very interesting coding scheme and crossoverperator. In summary, the main features of proposed GFS are asollowing:

it is based on the Pittsburgh classifier system model;it is a rule-based system as opposed to domain-based;the number of rules in each rule-set is allowed to vary, under theaction of crossover, rule creation and deletion operators, and acover operator;the system learns both fuzzy rules and fuzzy set membershipfunctions;rule and fuzzy set membership encodings are real-numberedrather than using bit strings;a crossover operator is employed which respects the fact thatgenes representing rules with overlapping fuzzy sets are epistat-ically linked.

The approach can be decomposed in the following steps:Step 1 – Rule set encoding on chromosomeThe approach employs same rule representation proposed by

arodi and Bonelli [35] with each rule, Rk, for an n-input, m-outputystem, expressed as:

k : ((xc1k, xw1k); (xc2k, xw2k); . . . ; (xcnk, xwnk)) → (yck, ywk) (4)

he bracketed terms represent the centers and widths of fuzzy setembership functions over the range of input and output variables.

he chromosome representing a complete rule-set is a variableength concatenated string of such fuzzy rules. Fig. 2 shows a 2-nput 1-output encoded chromosome.

This representation allows genetic operators to work on bothuzzy rule-sets and membership functions. In addition since fuzzyet membership functions are encoded together with each rule,ules are permitted to evolve with different degrees of vaguenessn the fuzzy sets they relate.

Step 2 – Generating the initial populationIn this step the algorithm randomly generates a population of

pop rule-sets, where each rule-set in the population is initialized toontain Ninit random rules although this is allowed to vary duringearning under the action of a cover operator and crossover. Therocess of generating random rules is as follows:

Generate input and output membership function centers ran-domly with uniform probability density from their extendedrange. Applying a minor extension on the range of initial mem-bership function centers beyond the range of the input and output

mputing 12 (2012) 700–711 703

spaces is used to improve the performance of the system at theextremes of these spaces.

• Generate initial membership function widths with uniform prob-ability density in the range.[

0,2(Xmax − Xmin)√

Ninit

](5)

where [Xmin, Xmax] is the range of the input or output variable.Choosing such range will encourage adequate coverage of inputand output spaces for each initial rule-set.

Step 3 – Calculate the fitness value of chromosomes in the cur-rent population

As regards the fitness function, it is based on an application-specific measure usually employed in the design of GFSs, the meansquared error (MSE) over a training data set, which is representedby the following expression:

MSE(Cj) = 1N

N∑i=1

(Yi − Pi)2 (6)

where Yi is actual value and Pi is the output value of ith trainingdata obtained from the fuzzy system using the RB coded in jthchromosome (Cj).

Step 4 – Produce new generation by means of genetic opera-tions

A generation strategy for replacement is adopted. In each gener-ation a specified percentage (namely 10% in our case) of the weakestmembers of the population will be replaced with the newly gen-erated rules, i.e. some of the weakest solutions will be deleted andsome new rules will be created instead. The adopted operators areas follows.

• Crossover operatorIn moving from the discrete to the fuzzy case, a further level of

interaction between rules encoded on the chromosome is intro-duced. Any two or more rules whose input fuzzy set membershipfunctions overlap are epistatically linked on the chromosomesince the crisp output value over the range of overlap of theinputs is determined by the combined action of all matched rules.Indeed, the identification of arbitrary input/output functionsusing fixed shape membership functions relies on this overlap. Acrossover operator which preserves rather than destroying theselinkages is likely to be a good one.

A novel crossover operator (called ordered two point crossover)is employed in this GFS which takes this observation to itsextreme conclusion. The crossover operator is based on the classi-cal two-point crossover but with an n-dimensional consideration(being n the number of input variables). First, the rules on eachchromosome are sorted according to the centers of the inputmembership functions. This introduces an association betweena rule’s input membership function center and its position onthe chromosome. Then, two random numbers are selected foreach input variable within its range. The parameters for ith inputvariable are calculated as follows:

C1i

= MINi + (MAXi − MINi) · (R1)1/n

C2i

= C1i

+ (MAXi − MINi) · (R2)1/n (7)

with [MINi, MAXi] being the domain of the variable and with R1and R2 being two random numbers uniformly generated in [0, 1].

The first offspring will contain rules from the first parent such

that

∀i,(

(xCik > C1

i ) AND (xCik < C2

i ))

OR(

(xCik + MAXi − MINi) < C2

i

)(8)

704 E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711

e of fuzzy system as chromosomes.

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The extracted rule bases of cluster 1 and cluster 2 are shown inFigs. 6 and 7, respectively.

Table 1Optimum features of GFSs.

GFS-optimum features WGFS (withoutclustering)

CGFS (with clustering)

Cluster 1 Cluster 2

Population size 100 100 100Initial number of rules per 13 9 7

Fig. 2. Coding knowledge bas

as well as rules from the second parent that do not satisfy thiscondition, i.e.,

∃i,(

(xCik ≤ C1

i ) OR (xCik ≥ C2

i ))

AND(

(xCik + MAXi − MINi) ≥ C2

i

)(9)

The second offspring will contain the remaining rules from bothparents.Mutation operator

The mutation operator used in this approach is considerablysimpler and applies real-number creep to fuzzy set membershipfunction centers and widths. The mutation operator picks a sin-gle rule at random from the rule-set. Next, either the center orwidth of one membership function within that rule is multipliedby a random number. Mutation is therefore used for fine tuningrather than for introducing radically different individuals into thepopulation.Selection operator

Selection for reproduction is rank-based.Cover operator

A cover operator is also proposed to ensure that all the inputdata is covered by at least a rule. The cover operator works asfollows: if a set of inputs is encountered which does not match anyrules in the rule-base, a new rule is created with input fuzzy setmembership function centers set equal to the unmatched inputvector; output membership function centers are set randomly inthe allowed range; and all membership function widths set asdescribed in previous steps.

Step 5 – Stopping criteriaIf the number of generations equals to the maximum generation

umber, then stop; otherwise go to step 3.

. Experimental results

For the purpose of validating the CGFS, in this section we usehe same dataset used by Cheng et al. [1]. This data set consistsf the number of monthly outpatient visits from the depart-ent of internal medicine in a hospital in Taiwan, from year

001 to 2005. The data set is divided into two sub-datasets: theraining dataset (2001/1/1–2004/12/31) and the testing data set2005/1/1–2005/12/31). Outpatient visits forecasting, in term ofnput, will be addressed using time lags of outpatient visits asnputs. We use 2 lags of outpatient visits as input variables (asheng et al. [1] did). So, CGFS is used for a projecting/reflectingction:

: (OV(k − 1), OV(k − 2)) → OV(k) (10)

here OV(k) is the number of outpatient visits in kth month. Fig. 3hows the number of outpatient visits in our case study.

Fig. 3. Number of monthly outpatient visits in a hospital in Taiwan.

3.1. Implementing CGFS for outpatient visits forecasting

In the first stage, we use SOM neural network to cluster train-ing dataset into sub-populations and reduce the complexity of thewhole data space to something more homogeneous. The total num-ber of training data is only 46, so it is not necessary to cluster thesedata into too many clusters. In our case we clustered data intotwo clusters. In the second stage we build a GFS for each clusterusing related training data. Finally, in the testing phase, the testset data is first assigned to the clusters (by means of the trainedSOM) then forecasting process is done by means of each cluster’sGFS. It should be noted that in order to investigate effects of clus-tering on improvement of GFS, we implement CGFS one more timewithout clustering concept (WGFS). To meet a robust and accu-rate model, different feature of parameters have been examined forCGFS, this process is called the tuning process. The tuned featuresof parameters are shown in Table 1.

Moreover, Fig. 4 visualizes the two clusters of data (related toCGFS).

The CGFS is applied for forecasting the outpatient visits and theresults are shown in Fig. 5 and Table 2.

individualNumber of generations 400 200 200Crossover probability 0.8 0.8 0.8Mutation probability 0.1 0.1 0.1

E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711 705

Fig. 4. SOM cluste

Table 2Forecasting results of CGFS for test data.

Month Actual Forecasted by CGFS Cluster

January-05 5920 5803.508 1February-05 5512 5623.224 1March-05 6548 5536.457 1April-05 5987 5721.429 1May-05 5638 5746.599 1June-05 5851 5593.902 1July-05 5514 5670.675 1August-05 5395 5534.897 1September-05 5598 5480.107 1October-05 5284 5501.474 1November-05 4545 5361.121 1December-05 4624 4624 2

Fig. 5. CGFS forecasted val

ring results.

The CGFS with parameters in Table 1 is the best CGFS that hasconcluded in tuning process. It is mentioned that different mix ofparameters for CGFS have tested and among them the parameter“initial number of rules per individual” has most effect in results.We run an experiment to test if this parameter has significant effectin accuracy of forecasted values. In this experiment different num-bers for “initial number of rules per individual” for cluster 1 is tested(in cluster 2 there is one test data and the GFS with 7 initial ruleshas high accuracy so there is no need for experiment this param-eter in cluster 2). If other parameters of GFS are set as Table 1,

Fig. 8 shows the results of forecasting with different CGFSs. In thiscase study we use robust error estimation functions such as Root

ues vs. actual values.

706 E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711

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results of the CGFSs are not significantly different. So we concludethat the results of proposed CGFS model are stable and choice ofparameters does not much effect in accuracy of model.

Table 3Results of Friedman test for ranking different CGFSs.

Model Sum (ranks) Mean (ranks)

CGFS6a 60.5 5.0417CGFS7 51.5 4.2917CGFS8 57.5 4.7917CGFS9 42.5 3.5417CGFS10 50.5 4.2083CGFS11 58.5 4.8750CGFS12 60.5 5.0417CGFS13 50.5 4.2083

Fig. 6. Fuzzy rule base and mem

ean Square Error (RMSE), Mean Absolute Error (MAE) and Meanbsolute Percentage Error (MAPE).

MSE =

√√√√ 1N

N∑i=1

(Yi − Pi)2 (11)

AE = 1N

N∑i=1

|Yi − Pi| (12)

APE = 100 × 1N

N∑i=1

|Yi − Pi|Yi

(13)

here Yi is the actual value and Pi is the forecasted value of ith testata obtained from CGFS model and N is the number of test data.he results are shown in Fig. 8.

We want to test the hypothesis that the choice of differentarameters for CGFS has not much effect to results of model.o meet this purpose, we apply one powerful rank-based non-arametric test called Friedman’s two-way analysis of varianceest [36], to rank the CGFSs and determine existence of differ-

nces among the performance of them (see Appendix A). Underhe null hypothesis, Friedman test states that CGFSs are equivalent,o a rejection of this hypothesis implies the existence of differ-nces among the performance of the CGFSs. We use relative error

ip functions of cluster 1’s GFS.

percentage of forecasted values of test data for different CGFSs forFriedman test. This value for each observation (i) is computed by:

errori =∣∣∣Predictedi − Actuali

Actuali

∣∣∣ × 100 (14)

Results of Friedman test are shown in Table 3.In our case, the Friedman test indicates that CGFS9 is relatively

better than the others but significant differences in the resultsare rejected and as its consequence we may figure out forecasting

Friedman value 4.242420.7514

a CGFSi means CGFS with “initial number of rules per individual” parameter equalto i.

E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711 707

Fig. 7. Fuzzy rule base and members

Table 4Evaluation of GFS vs. other methods.

Method MAPE (%)

Chen [4] 9.97Yu [5] 8.60Cheng et al. [1] 6.21

3

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TC

WGFS (CGFS without clustering) 6.03CGFS (proposed model) 4.34

.2. Performance analysis of CGFS

For the purpose of evaluating forecasting accuracy of CGFS,e will compare outputs of best CGFS obtained in tuning process

CGFS9) with other models which were applied on the same datasety the other researchers. We perform the comparison by MAPEalue because it is the criteria that used in the reference articlend is the most suitable method to estimate the relative error [37].

ummary of CGFS evaluations in comparison with the other modelss shown in Table 4.

Regarding to Table 4, CGFS has improved the forecastingccuracy of outpatient visits and outperforms previous methods.

able 5GFS evaluation vs. WGFS.

Error estimation method Kashani Tohid

CGFS WGFS CGFS

MAPE 4.65 7.3 5.43

RMSE 87.18 123.75 1495

MAE 63.81 95.05 1016

hip function of cluster 2’s GFS.

Namely, it has made 30% improvement in the best obtained MAPEvalue which was provided by Cheng et al. [1]. Moreover, by compar-ing MAPE values of CGFS and WGFS we find out that, data clusteringhas significant impact on accuracy of GFS (i.e. 28% improvement inMAPE value).

3.3. Forecasting of the monthly outpatient visits from four bighospitals in Iran

According to the comparative results shown in the previous sec-tion, it could be concluded that the CGFS model is more accuratethan the others in forecasting outpatient visits. So in this sectionwe apply the CGFS and WGFS that obtained as two best mod-els at previous section to forecast the monthly outpatient visitsfrom Kashani hospital of Shahrekord city in Charmahal-o-Bakhtiariprovince and three big hospitals (Tohid, Ghorveh and Saghez) inKordestan province of Iran. These are the largest specialist and

super specialist hospital in those provinces and consist of severalwards such as orthopedic, urology, men surgery, women surgery,neurology, heart surgery, burn, I.C.U. and post I.C.U.

These hospitals in their vision context are going to:

Ghorveh Saghez

WGFS CGFS WGFS CGFS WGFS

7.59 6.1 7.55 5.05 7.791796 1492 1620 909 15011433 808 1159 603 859

708 E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711

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Fig. 8. Evaluatio

Be the best health service provider throughout the province intwo respects: excellency and value for money policy.Be the first choice of patients, physicians and staffs.Be pioneer in utilization of the high-tech medical care.Be a benchmark for hospital administration in the province.Have the best physician and the other staff by improving theirknowledge and skill.

However according to benefits of forecasting outpatient visitsentioned in section 1 and need for this forecasting system in these

ospitals stated by managers of hospitals, we use the historical dataccording to the volume of monthly outpatient visits from June

007 to October 2010 of these hospitals to construct an outpatientisits forecaster system.

Outpatient visits forecasting in terms of input, will be addressedsing two time lags of outpatient visits as Eq. (10) and in these case

istics for CGFSs.

we clustered data into two clusters. Forecasting results are shownin Fig. 9.

The result of evaluation statistics is shown in Table 5.We will choose the best fitted model out of WGFS and CGFS by

hypothesis testing. To meet this purpose following hypothesis isproposed:

H0. There is no difference among prediction accuracy of WGFSand CGFS.

H1. Difference exists among the prediction accuracy of the twomodels.

Since data used for prediction in both models are the same, wecarry out paired t-test (two samples for mean) on prediction accu-racy (relative error percentage) to test the hypothesis for all cases.The results of paired t-tests are shown in Table 6.

E. Hadavandi et al. / Applied Soft Computing 12 (2012) 700–711 709

Fig. 9. CGFS forecasted values vs. actual values for all cases.

Table 6The results of paired t-test for all cases.

Hospital name Mean of deviation Std. deviation t-Stat P-value df Conclusion

Kashani −2.65 4.935 −3.442 0.0013 40 �WGFS > �CGFS

cdcswa

4

isin

•

Tohid −2.15 3.42

Ghorveh −2.018 5.17

Saghez −2.805 9.46

As it is shown, since P-value < 0.02 so H0 is rejected in level ofonfidence ̨ = 0.02. The evidence indicates that the average pre-iction error of CGFS is significantly lower than that of WGFS for allases. Then, CGFS will be considered as the preferred model for con-tructing outpatient visits forecaster system of these hospitals. Alsoe may conclude that data clustering has remarkably improved

ccuracy of forecasts.

. Conclusion

This paper presented a novel approach (CGFS) based on combin-ng data clustering and genetic fuzzy systems for building an expertystem to forecast outpatient visits in hospitals, with the aim ofmproving forecasting accuracy. Proposed CGFS has the followingovel features:

By using SOM clustering, we divide the data into sub-populationsand reduce the complexity of the whole data space to something

−4.11 0.00017 40 �WGFS > �CGFS

−2.557 0.01422 40 �WGFS > �CGFS

−2.14 0.01921 40 �WGFS > �CGFS

more homogeneous and reduce effects of noisy data. Its conse-quence is improving forecasting accuracy.

• GAs have been demonstrated to be a powerful tool for automatingthe definition of the fuzzy knowledge base system. Proposed CGFSuses genetic algorithms for evolving knowledge base of the fuzzyexpert system.

• CGFS is able to handle complex and nonlinear time series withlimited available data.

• The novel representation of chromosomes in CGFS allows geneticoperators to work on both fuzzy rule-sets and membership func-tions simultaneously. In addition since fuzzy set membershipfunctions are encoded together with each rule, rules are permit-ted to evolve with different degrees of vagueness in the fuzzy setsthey relate. These characteristics have yielded a very powerfulsearch algorithm.

• Policy makers of healthcare centers are capable of han-

dling non-linearity, complexity as well as uncertainty thatmay exist in actual datasets with respect to outpatient vis-its due to erratic responses and measurement errors. Theproposed model will provide decision makers with improved

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10 E. Hadavandi et al. / Applied S

estimation and decreased error in complex and uncertainenvironment.

For the purpose of evaluating the proposed approach we appliedt for forecasting outpatient visits of the department of internal

edicine in a Hospital in Taiwan and then we use it for constructingn outpatient visits forecaster for four big hospitals of Iran. Resultshowed that CGFS has higher accuracy relative to the other methodsn literature in case of Hospital in Taiwan. Also implementing CGFSor constructing outpatient visits forecaster in four hospitals in Iranre very successful and promising. Therefore CGFS can be used as auitable forecasting tool for outpatient visits forecasting problems.

ppendix A.

Friedman test ranks the algorithms so the best performing algo-ithm gets the rank of 1, the second best rank 2, and so on. Letji

be the rank of the jth of k algorithms on the ith of N observa-ions (treatments). The Friedman test compares the average ranksf algorithms, Rj = (1/N)

∑Ni=1rj

i. Under the null hypothesis, which

tates that all the algorithms are equivalent and so their ranks Rjhould be equal, the Friedman statistic:

2F = 12N

k(k + 1)

⎡⎣ k∑

j=1

jR2j − k(k + 1)2

4

⎤⎦

s distributed according to �2F with k − 1 degrees of freedom.

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Esmaeil Hadavandi received the Bachelor’s degree inApplied Mathematics from Tarbiat Moallem University ofTehran (TMU) in 2007, the Master’s degree in IndustrialEngineering from Sharif University of Technology (SUT)in 2009. He is author or co-author of about 20 scientificpapers in international journals and international confer-ences. His research is mainly in the field of Hybrid SoftComputing models, Data Mining, Economic Modeling andOperation Management.

Hassan Shavandi received B.Sc. degree in Industrial Engi-neering from Azad University of Qazvin in 1996. Afterthat he continued his graduate education in Sharif Uni-versity of Technology in Industrial Engineering and gainedhis PhD in May 2005. Hassan Shavandi joined to Depart-ment of Industrial Engineering in Sharif University ofTechnology as faculty member in 2006 and now he isan associate professor and teaches the courses “Pricingand Revenue Management”, “Fuzzy Logic and its Applica-tion”, “Management Information Systems” and “Principlesof Marketing”. Hassan Shavandi has many researches and

published papers in the field of fuzzy logic as well asapplied operations research. He has also a published book

in Farsi with the title of “Fuzzy Sets and its Applications in Management and Indus-trial Engineering”.

oft Co

from Tarbiat Moallem University in 2008. He is now Ph.D.student of Applied Mathematics at Azad University in Iran.His research is mainly in the field of Data EnvelopmentAnalysis, Operation Research, Fuzzy Logic, Soft Comput-ing, and Data Mining.

E. Hadavandi et al. / Applied S

Arash Ghanbari obtained his M.Sc. degree in Indus-trial Engineering /Systems Engineering from Universityof Tehran (UT), in 2010. His current research interestsinclude Artificial Intelligence, Soft Computing, Forecast-ing and Modeling. With a particular focus on developinghybrid soft computing models for forecasting time seriesdata. He is currently involved in research and develop-ment projects about Data Mining and specifically Noise

Filtering for improvement of Artificial Intelligence tech-niques. He is the author or co-author of around 30 papersin recognized international journals and conferences. Hehas also served as the reviewer of several internationaljournals and conferences.

mputing 12 (2012) 700–711 711

Salman Abbasian-Naghneh received the Bachelor’sdegree in Applied Mathematics from Shahrekord Univer-sity in 2005, the Master’s degree in Applied Mathematics