ORIGINAL PAPER

Tehran’s seismic vulnerability classification using granularcomputing approach

Hadis Samadi Alinia & M. R. Delavar

Received: 16 October 2010 /Accepted: 9 October 2011 /Published online: 27 October 2011# Società Italiana di Fotogrammetria e Topografia (SIFET) 2011

Abstract Tehran, capital of Iran, is located on a number ofknown and unknown faults which make this mega cityexposed to huge earthquakes. Determining locations andintensity of seismic vulnerability of a city is considered as acomplicated disaster management problem. As this problemgenerally depends on various criteria, one of the mostimportant challenges concerned is the existence of uncer-tainty regarding inconsistency in combining those effectivecriteria. The emergence of uncertainty in seismic vulnera-bility map results to some biases in risk management whichhas multilateral effects in dealing with the consequences ofthe earthquake. To overcome this problem, this paperproposes a new approach for Tehran’s seismic vulnerabilityclassification based on granular computing. One of themost significant properties of this method is inference ofaccurate rules having zero entropy from predefined classi-fication undertaken based on training datasets by the expert.Furthermore, not-redundant covering rules will be extractedfor consistent classification where one object maybeclassified with two or more nonredundant rules. In thispaper, Tehran statistical zones (3,173 according to 1996census) are considered as the study area. Since this city hasnot experienced a disastrous earthquake since 1830, thiswork’s results is the relative accurate with respect to theresults of previous studies.

Keywords Granule network . Decision rules .

Classification . Entropy measurement . Seismicvulnerability . Geospatial information system

Introduction

Iran is one of the seismically active areas of the world dueto its position in the Alpine-Himalayan mountain system. Alot of strong earthquakes in this area have caused a high tollof casualties and extensive damage over the last centuries.Tehran, Capital of Iran, is located at the southern foot of theAlborz Mountains and a large fault is located in thismountain. This city, virtually surrounded by a number ofknown and unknown faults, has suffered huge earthquakedisasters in cycles of approximately every 150 years. Sincethere have not been any large earthquakes (greater than 6Richter) in Tehran in the past 170 years, local seismologistsbelieve the possibility of a huge earthquake in Tehran in thenear future (JICA 2001). Thus, there is a need to developand implement appropriate frameworks and technologies torespond to earthquake disaster. Production of seismicvulnerability map could help local and national disastermanagement organizations to achieve this goal (Aghataheret al. 2005).

Several researches have done risk assessment in Tehranlike the Geotechnical Microzonation carried out by Inter-national Institute of Earthquake Engineering and Seismol-ogy (IIEES; Shafiee et al. 2011; Zare et al. 1999; Zare2003; Jafari et al. 2004) and Japan International Coopera-tion Agency (JICA 2000) microzoning maps.

One of the most important challenges concerning solvingsuch a multicriteria decision problem is the existence ofuncertainty regarding inconsistency in the process ofdecision making. Indeed, a recommendation to the problem

H. Samadi Alinia (*)GIS Division, Department of Surveying and GeomaticsEngineering, College of Engineering, University of Tehran,Tehran, Irane-mail: Alinia_202000@yahoo.com

M. R. DelavarCenter of Excellence in Geomatics Engineering and DisasterManagement, Department of Surveying and GeomaticsEngineering, College of Engineering, University of Tehran,Tehran, Iran

Appl Geomat (2011) 3:229–240DOI 10.1007/s12518-011-0068-7

is offered to the decision maker (DM), in terms ofvulnerability degree of urban areas. The classical methodscan be of little help when used in such environments.

Some multicriteria evaluation methods have recentlybeen proposed to handle some aspects of uncertainties inthe process of producing the seismic vulnerability map forTehran. For instance, Aghataher et al. (2005) implementedenhanced analytical hierarchical approach for weighingvulnerability factors and for evaluating their uncertaintythrough fuzzy logic. He focuses especially on peoplevulnerability in Tehran. The other example for physicaland people seismic vulnerability assessment is the frame-work proposed by Silavi. In this framework, she examinesthe potential of a couple of fuzzy logic based improvedspatial analysis processes including fuzzy and intuitionisticfuzzy (IF) improved analytical hierarchy process (AHP)approach (Silavi et al. 2006). Also, in this framework, twopessimistic and optimistic maps were obtained. In the otherframework which was implemented by Amiri, urban areasof the city of Tehran are sorted in respect of their seismicvulnerability grades. He used dominance-based rough set(DRSA) to approximate partition of a set of predefined andpreference-ordered classes (vulnerability grades). Thisapproximation is a number of decision rules in the formof “IF–THEN” logic. Some of these rules are exact and theothers are probabilistic. In this approach, it is possible tomeasure the accuracy of approximation (Amiri et al. 2007).Dempster–Shafer Analytic Hierarchy Process (DS/AHP) isan approach which Jahankhah et al. (2009) is used to modeluncertainty based on independent assumption of intuitionsources that is not established in data such as geospatialinformation.

Granular computing approach is proposed in this paperto overcome the limitation of the abovementioned existingalgorithms. It can be regarded for learning classificationrules by considering the two basic issues: concept forma-tion (making granules) and concept relationships identifi-cation (relationship between granules). One of thesignificant features of this method with respect to previousstudies is inference of more compatible rules having zeroinconsistency extracted from existing training databases.Furthermore, in this approach, nonredundant covering ruleswill be extracted for consistent classification where oneobject maybe classified with two or more nonredundantrules.

Granular computing may be regarded as a label oftheories, methodologies, techniques, and tools that makeuse of granules, i.e., groups, classes, or clusters of auniverse in the process of problem solving (Yao 2000,2004). Its concepts, i.e., problem solving with differentgranularities, have been accrued in many fields, such asinterval analysis (Moore 1966), rough set theory (Pawlak1982), fuzzy sets (Zadeh 1997), clustering (Zhong et al.

2007), problem solving (Lin et al. 2002), Dempster–Shafertheory of evidence (Shafer 1976) and many others. Theterm “granular computing” was first suggested by T.Y. Lin(Zadeh 1998). A number of researchers have examinedgranular computing. Yao and Yao presented a granularcomputing view to classification problems and proposed agranular computing approach for classification (Yao andYao 2002a, b).

The main objective of this paper is to exhibit howgranular computing approach can be used for the inferenceof seismic classification rules and to evaluate the accuracyof the method in respect to previous researches. Geospatialinformation system (GIS) is used as an implementationframework which extracted decision rules to be applied tothe whole urban areas.

There are two aspects of a concept, the intension andextension of the concept (Demri and Orlowska 1998; Wille1992). In this paper, the concept of seismic vulnerabilitycan be exemplified at two parts, extension, i.e., a set ofobjects as instances of prespecies category of seismicvulnerability and intension, consisting of all effectiveattributes, which is valid for all those urban areas wherethe concept applies (Samadi Alinia 2010). In this paper,urban areas are considered as objects and six physicallyvulnerability criteria are taken into account as attributes ofthe objects. An object must be described in terms of a fixedset of attribute, each with its own set of possible values. Forexample, in this paper, “Slope” might be an attribute with aset of possible values {low, moderate, high, very high} fora specific urban area.

The schema of this work starts with an overview of thestudy area and data employed as the input dataset to thegranular computing algorithm. At the end of this chapter, itcan be concluded that an information table provides aconvenient way to describe a finite set of objects, called auniverse, by a finite set of attributes. The next sectionelaborates on construction of a granule decision tree, itsability to evaluate its classification performance level bylevel and finally extract more consistent classification rules.It is demonstrated how granules is autoconstructed from theuniverse in multilevel of construction and which measuresshould be employed to find the most promising attribute-value pairs at each level. The underlying idea is that highsupport and confidence measures of the rules and theminimum values of entropy associated with granules have acritical role in extracting the most compatible rules. Thissection is dealt with proposing conditions to modify thegranular decision tree until a consistent classification isobtained.

In Section 4, the granular computing approach isexamined for the seismic vulnerability classification ofTehran. In this section, the constructed seismic granule treeis employed for seismic vulnerability classification of

230 Appl Geomat (2011) 3:229–240

Tehran Metropolitan Area (TMA). As a result of thissection, the produced Tehran’s seismic vulnerability mapwill be presented. In Section 5, conclusion and somesuggestions for further researches are presented.

Data preparation

Study area

The study area is Tehran, capital of Iran. Tehran is locatedat the southern foot of the Alborz Mountains, which extendto the Alps-Himalaya orogenic zone and has a populationmore than 10 million, consisting of Tehran city and itsadjacent zone of influence. This city, virtually surroundedby a number of faults, has suffered large earthquakedisasters in cycles of approximately every 150 years. Afew important known faults are as follows (Silavi et al.2006)

Mosha Fault

The Mosha Fault which is situated toward the northern sideof Tehran is one of the major active faults in Central Alborz(Fig. 1) based on its strong historical seismicity and itsobvious morphological signature. It seems to be one of themost active, experiencing several earthquakes of magnitudegreater than 6.5 in the years 958, 1,665, and 1,830(Berberian and Yeats 2001).

The length of this fault is approximately equal to150 km, and by considering ~ N100E trending fault, thisfault can be regarded as an important potential seismicsource that threatens the Iranian metropolis (Nazari et al.2007). It is an E–W trending left lateral strike–slip faultdipping steeply to the North and having a slight normalcomponent (Ritz et al. 2003).

North Tehran Fault

The North Tehran Fault is located at the southernmostpiedmont of Central Alborz. It is 90 km long and located onthe north of Teheran. It has E–W to ENE–WSW strike and hasthrust mechanism. It stands out as a major active faultthreatening directly the city of Tehran and would have beenthe source of several major historical earthquakes in the past.It can be assumed that the dip of NTF is milder than 75°,because this fault is a branch of Mosha Fault. Contrary toMosha Fault, this quaternary alluvium does not have a distinctfault scarp (Berberian and Yeats 1999). The historical activityof the fault is not yet proven although some authors suspectthat the 855 and 856 AD events could be associated to thefault (e.g., Berberian and Yeats 1999, 2001).

South and North Ray Faults

The South and North Ray Faults are the most prominentfaults in the southern plains in Tehran (JICA 2000). TheNorth Ray Fault is located on south of Tehran City andnorth of Shahre Ray City. The length of fault is 16.5 kmand direction is W–E and dip of fault is toward north. TheSouth Ray Fault is also located on south of Tehran Citywith more than 18 km length and direction is ENE–WSW(Berberian 1976). Figure 1 illustrates the relative locationof faults within TMA.

Among these main faults, the north Tehran fault situatedtoward the northern side of Tehran has the potential togenerate MW=7.2 (JICA 2000), respectively, whichaccording to the earthquake scenarios developed under theJICA-CEST project “Study on the seismic microzoning ofthe greater Tehran area,” 1999–2000, could lead to manyvictims. Seismologists believe that a strong earthquake willstrike Tehran in the near future because the city has notexperienced a disastrous earthquake since 1830 (JICA

Fig. 1 Tehran’s faults (JICA2000)

Appl Geomat (2011) 3:229–240 231

2000). Therefore, in this research, the result of north Tehranfault hazard analysis of JICA-CEST project is applied to thevulnerability assessment process, and activation of otherfaults has been ignored. It is assumed that the northern faultof Tehran is activated and then a seismic physicalvulnerability is gained.

As mentioned before, all urban areas of TMA predefinedwas selected for the purpose of this study. Tehran is partitionedto 3,173 statistical units according to 1996 census. The studyarea is located between 51°5′E, 51°37′E latitude and 35°49′N,35°33′N longitude. Figure 2 illustrates the study area inwhich the location of the north Tehran Fault is shown.

Data

This paper focuses on consistent knowledge discovery bymining rules in the framework of granular computingapproach. Because of shortage of enough historical damagedata in Tehran, this paper attempts to outline a proposedstrategy to assess earthquake vulnerability based on somemore critical parameters in which the statistical informationare from the 1996 census.

One of the most important reasons for severe losses inearthquake risks is the high level of physical vulnerabil-ity of buildings in urban and rural areas. Because of oldand nonstandard buildings in Tehran especially in thesouth and center of Tehran, it is assumed that sixparameters have physical seismic vulnerability effects.These criteria include earthquake intensity in terms ofModified Mercalli Intensity scale (MMI) unit (it is

assumed that the north fault of Tehran is activated),which describes the seismic potential of the fault foreach area and slope, percentage of weak buildings lessthan four floors, percentage of more than four-floorbuildings, percentage of buildings built before 1966, andpercentage of buildings built between 1966 and 1988identify account for the vulnerability of the area (Amiriet al. 2007; Silavi et al. 2006; Samadi Alinia 2010).

The raw data is obtained from the Statistical Center ofIran. These data have been prepared in the GIS databaseframework and values of effective variables were compiledin Arc/Info grid format to facilitate applying the rules. Thecell size of the raster was considered 15×15 m based on thescale of the map employed for the classification. Theprojection system and datum of all layers were defined inWGS_1984. Figure 3 illustrates the prepared map in rasterformat for each parameter.

For simplification, the titles of all criteria are given asfollows in the rest of paper:

MMI Earthquake intensitySlope Slope (°)Build_less4 Percentage of weak buildings less than four

floorsBuild_more4 Percentage of more than four-floor buildingsBef 66 Percentage of buildings built before 1966Bet 66–88 Percentage of buildings built between 1966

and 1988

Knowledge extraction from large dataset would be verytime-consuming and the results would have inconsistency.

Fig. 2 Study area (SamadiAlinia 2010)

232 Appl Geomat (2011) 3:229–240

To cover these kinds of problems, in this research, twosubsets of the original data are selected based on unalignedstratified random sampling as train and test dataset. It is amethod for selecting sample dataset, in which layers in GISare first divided into subgroups, and then random samplesare drawn from each groups. The advantages of this methodare increasing the likelihood of selection of all kinds of dataand evaluate the accuracy of the result of classification. Inthis research, 113 urban areas are selected as trainingdataset and 30 urban areas as test dataset from 3,173 wholeurban areas (Fig. 4). Because of shortage of enoughhistorical damage data in Tehran, these selected data islabeled by a seismologist expert in terms of their seismicvulnerability degree.

Information table

Information tables of training dataset are used as basisknowledge in granular computing models. It provides aconvenient way to describe a finite set of objects called auniverse by a finite set of attributes.

Definition of an information table is shown in Eq. 1:(Pawlak 1991; Yao and Zhong 1999)

S ¼ U ;At; L; Vaja 2 Atf g; Iaja 2 Atf gð Þ ð1Þ

where U is a finite nonempty set of objects, At is a finitenonempty set of attributes, L is a language defined by usingattributes in At, Va is a nonempty set of values of a∈At, Ia:

Fig. 3 Grid dataset for whole urban areas in Tehran from seismic vulnerability effective parameters

Appl Geomat (2011) 3:229–240 233

U→Va is an information function that maps an object of Uto exactly one possible value of attribute a in Va.

By considering an attribute a∈At, an object x∈U takesonly one value from the domain Va of a. Let a(x)=Ia(x)denote the value of x on a. So, for an attribute a∈At and x,y∈U, an equivalence relation Ea is given by:

xEay , aðxÞ ¼ aðyÞWith respect to all attributes in A, x and y are

indiscernible, if and only if they have the same value forevery attribute in A (Yao 2004???). Therefore, a language Lis defined for describing objects of the universe in aninformation table. The decision logic language (DLlanguage) studied by Pawlak (1991) is adopted. This logiclanguage is defined for the information table to provideformal descriptions of various notions. The meaning offormulas is interpreted using subsets of objects. Thus, theintension of a concept can be expressed by a formula of thelanguage, while the extension of a concept is presented asthe set of objects satisfy the formula.

This formulation enables us to study formal concepts ina logic setting in terms of intension and also in a set-theoretic setting in terms of extensions.

By considering the definition of information table, theinformation table of training dataset of this research isconstructed from 113 training data which were arranged in113 rows of objects and seven columns of attributes. It isassumed that there is a unique attribute class taking classlabels as its value. The set of attributes is expressed as At=FU{class}, where F is the set of attributes used to describe

the objects and {class} is a decision attribute. The goal is tofind classification rules in the form ofϕ ) classci, where ϕis a formula over F and ci is a class label. In this research,the grade of seismic vulnerability, which was predefined bya seismologist expert based on six criteria, is considered asa column of “class” in the information table. Each record inthe table is a value of attribute in human language form.Each class is expressed by a natural language. These classesfor all criteria are obtained from natural break approach.For example, mean slope is categorized to: low [0–3.86],moderate [3.86–12.11], high [12.11–23.35], and very high[23.35–45]. Table 1 illustrates a part of the constructedinformation table of this research. Out of 113 rows, tenrows of training dataset of seismic vulnerability informationtable is selected and illustrated in Table 1.

In this case, five classes for discerning degrees ofseismic vulnerability between the groups of urban blocksare considered including very high vulnerable, highvulnerable, moderate vulnerable, low vulnerable, and verylow vulnerable. In order to bring comfort to the process,seismic vulnerability is scaled as: very low vulnerable = 1,low vulnerable = 2, moderate vulnerable = 3, highvulnerable = 4, and very high vulnerable = 5.

Granular computing approach

In spite of classical methods in which only one attribute isselected at each step (Ganascia 1993), granular computinguse the strategy of granule center in which one granule isdefined by an attribute–value pair at each step (Samadi

Fig. 4 Training urban areas(113) and test urban areas (30)

234 Appl Geomat (2011) 3:229–240

Alinia et al. 2010a). In this approach, a family of granulesdefined by values of an attribute, at each step, is concentratedon the selection of a single granule (Yao and Yao 2002a)instead of focusing on the selection of a suitable partition.

In a granule network, each node is labeled by a subset ofobjects named as a granule. The arc leading from a largergranule to a smaller granule is labeled by an atomicformula. In the Decision language, an atomic formula isgiven by a=v, where a∈At and v 2 va. A smaller granule isobtained by selecting those objects of the larger granule thatsatisfy the atomic formula. The family of the smallestgranules thus forms a conjunctively definable covering ofthe universe.

Inference of classification rules

To construct a granule network, it is required that at first theuniverse be divided into groups or partitions of the sameclass with a set of atomic formula of attribute values. A rulecan be expressed in the form, Φ⇒Ψ, where Φ and Ψ areintensions of two concepts. In many studies of machinelearning and data mining, a rule is usually paraphrased byan IF–THEN statement, “if an object satisfies Φ, then theobject satisfies Ψ.” The interpretation suggests a kind ofcause and effect relationship between Φ and ψ (Yao 2001).For this, some measures for a single-granule relationshipbetween two granules and relationship between a granuleand a family of granules are applied automatically by thegranule network algorithm. These measurements areexplained in the following three sections.

Measures of a single granule (generality)

Generality indicates the relative size of the granule. Agranule defined by the formula is more general if it coversmore instances of the universe.

The quantity may be viewed as the probability of arandomly selected object satisfying the formula (Yao andYao 2002a). Equation 2 shows the fraction of the size of agranule to the size of universe.

G ϕð Þ ¼ m ϕð Þj jUj j ð2Þ

Measurements on relationship between granules

Confidence or absolute support

This is defined as the fraction of instances that are correctlyclassified by the rule among the instances for which itmakes any prediction. Thus, it is a measure of thecorrectness or the precision of the inference. If the quantityof the confidence of a rule is kept high, then less number ofassociation rules will be mined, but their predictionaccuracy will be quite high (Zhao et al. 2007).

As Eq. 3 illustrates, the quantities can be computed by afraction of number of samples that satisfies the THEN partof the rule, to the number of samples that satisfy only the IFpart of association rule (Yao and Yao 2002a; Samadi Aliniaet al. 2010b).

Confidence class ¼ cija ¼ vð Þ ¼ p class ¼ cija ¼ vð Þ ð3Þ

Coverage

This is a measure of the applicability or recall of theinference. It indicates fraction of data in a class correctlyclassified by the rule (Yao and Yao 2002a).

The quantities can be computed by a fraction of anumber of samples that satisfy the THEN part of the rule, tothe size of training data with the same class label as the ruleconsequent. Equation 4 indicates how coverage can becomputed (Zhao et al. 2007):

Table 1 Seismic vulnerabilityinformation table for ten urbanareas

Object Slope MMI Build less4 Bef 66 Bet66–88 Build more4 Class

U1 Low High Low Medium Medium Very high 5

U2 Low High Low High Low Very high 4

U3 Low High Low Very high Low High 4

U4 Low High Very high Very high Low Medium 3

U5 Medium Medium High High Very high Very high 4

U6 Low High Very high Low High Low 2

U7 Medium Medium Very high Low Very high Low 4

U8 Medium Medium Medium Low High Low 2

U9 Low Medium High High Low Medium 3

U10 Low High Low Medium Low Very high 5

Appl Geomat (2011) 3:229–240 235

Coverage a ¼ vjclass ¼ cið Þ ¼ p a ¼ vjclass ¼ cið Þ ð4ÞIn the granule network algorithm, a rule with confidence

equal to one and high coverage nearest to one, consideringany redundancy, is selected as a decision rule. It is obviousthat more information with high quality about a conceptwill be inferred using granules if the granule tree coversboth a high absolute support and a high coverage.

Conditional entropy

It provides a measure that is inversely related to the strengthof the inference. This measurement which depends on theconfidence is a most commonly used measure for selectingan attribute value in the construction of decision tree forclassification (Quinlan 1983).

If one assumes the connection between two partitions ofthe universe, namely, Φ⇒Ψ, the conditional entropy H(Ψ|Φ)is computed by Eq. 5 (Zhao et al. 2007):

Entropy a ¼ vð Þ¼

XCI2vclassp class ¼cija ¼ vð Þ log class ¼ cija ¼ vð Þ

ð5ÞIf an object satisfies the formula of attribute value, one

can identify one equivalent class in which the objectbelongs with no uncertainty. In this case, confidence ofthe formula for at least one equivalent class is 1.

Seismic vulnerability granule network

To produce a seismic vulnerability classification with mini-mum uncertainty, it is required to find a subset of attributevalue with high coverage, confidence, and minimum entropy.

In this research, automatic inference of classificationrules for seismic vulnerability classification of tehran usinggranular computing algorithm involves applying concepts,such as generality, confidence, coverage, and entropy(previously defined), in eight important steps as follows:

(1) Load the training dataset.(2) Set U (the training dataset) as the root node of granule

tree at the initial stage.(3) Construct the family of basic concepts with respect to

atomic formulas:

BCðUÞ ¼ a ¼ v;m a ¼ vð Þ½ �ja 2 C; v 2 vaf g(4) Set the granule network to GN = ({U}, ϕ), which is a

graph consisting of only one node and no arc.(5) Set the activity status of U.(6) Select the BC = [a = v, m(a = v)] with maximum value

of fitness with respect to U.

(7) Select the BC = [a = v, m(a = v)] with maximum valueof fitness with respect to U.

(8) While the set of nonactive nodes is not a nonredundantcovering solution of the consistent classificationproblem, do:

(8-1) Select the active node Nwith the maximum value ofactivity (maximum entropy, minimum coverage).

(8-2) Compute entropy and generality for the activenode with respect to all remained attribute values.

(8-3) Select the basic concepts with minimum inter-section (least overlap) with the union of allnonactive nodes in granule tree.

(8-4) Select the basic concepts BC = [a = v, m(a = v)]with minimum entropy among granules in 8–3.

(8-5) If there is more than one concept selected in 8–4, the one with the maximum coverage of theseconcepts with respect to all considered classes isselected.

(8-6) Modify the granule network GN by adding thegranule N∩m (a = v) as a new node, connectingit to N by arc, and labeling it by a = v.

(8-7) Set the activity status of the new node.(8-8) Update the activity status of N.

(9) Export a granule tree and its corresponding classificationrules.

In the proposed algorithm, four parameters, such asgenerality, coverage, confidence, and entropy, is computedstep by step based on a need for more information to selectmore consistent and high-quality granules. It is clear thatthis decision tree will give nonredundant covering solutionin a shorter time than other existing algorithms, becausethis algorithm automatically select more appropriate pa-rameter based on the need. Furthermore, this algorithm atthe end of each level can recognize which granule is moreappropriate to be broken down first until it reaches to anonactive granule. The active and nonactive nodes at alevel should be characterized by considering two condi-tions. A granule is nonactive if it has two conditionsincluding (i) the granule is a subset of a unique class and(ii) the union of all granules at a low level covers the rootgranule. Thus, an active granule will be further dividedthrough efficient measures. In the used algorithm in thisresearch, the construction of the tree are continued until allgranules reaches zero entropy, in which union of allnonactive granules be equal to the universe set. On theother hand, after union of all nonactive granules in alllevels, cover the universe set, construction of decisiongranule tree would be stopped. So the tree providesinformation in the form of “IF–THEN” statements.

By running the algorithm on 113 urban areas, 65 rulesare inferred at six levels. Union of inactive granules at sixlevels covers the universe set. Each node of the granule

236 Appl Geomat (2011) 3:229–240

decision tree is labeled by a value of attribute and eachbranch is labeled by a value of the parent attribute.

The seismic vulnerability decision tree extracted fromthe sample information table illustrated in Table 1 isdemonstrated in Fig. 5.

In the constructed decision tree (Fig. 5), each non activegranule is labeled by its class value. The union of all nonactive granules in the two levels forms a nonredundantcovering solution of the consistent classification problem,meaning that the collection of the subsets derived by deletingany one of the granules is not a covering, and the union of allinactive subsets in the two levels forms the universe set.

Seismic vulnerability classification

Producing seismic vulnerability map using the inferredrules follows five sequential steps including (1) preparingdata grids from values of considered criteria (Fig. 3), (2)integrating rules to produce seismic vulnerability, and (3)analysis of the accuracy of the results.

In Step 1, the processing of spatial data and thegeneration of the input layers were established within aGIS framework exhibiting different criteria. All databelonging to the urban areas in vector format wereconverted to raster format (Fig. 3). The projection systemand datum of all layers were defined in WGS_1984. In Step2, the inferred rules are applied to the test urban areas (31urban areas). In this step, the resulted rules are integrated bymultiplying them to their related risk weight which wasconsidered the class labels. The accuracy of the results iscomputed by k

kþn formula in Step 3 (Zhao and Yao 2005),

where k is the number of objects classified correctly by arule, meaning the classified objects are completely withinthe related class, and n is the number of objects thatclassified incorrectly. The average accuracy of the resultsobtained by the extracted granule network is 72%. Thenthese high accuracy rules will be applied on the whole

urban areas of Tehran (3,173 urban areas) to produce theseismic vulnerability map.

Seismic vulnerability map for the considered study areais produced by employing the 65 inferred decision rules andis illustrated in Fig. 6.

As this map shows, by considering the six effectiveparameters, most of urban areas of Tehran have moderateseismic vulnerability. The frequency of urban areas inrespect of their seismic vulnerability degree obtained bygranular computing approach is shown in Fig. 7.

It can be concluded that 1,023 urban areas of the city,which most belong to the 6th, 7th, 8th, 10th, 11th, and 4thmetropolitan areas and include 32%of whole urban areas ofthe city, have moderate seismic vulnerability degree. Alsoby these results, 17% of whole urban areas of the city aremembers of the class very high based on granularcomputing classification approach. These areas most belongto the 12th and 16th metropolitan area of the city. As it wasexpected, the urban areas located in the center of the citywere high vulnerable rather than other urban areas in thecity due to existing old and nonstandard buildings.

Since this city has not experienced a disastrous earth-quake since 1830, the relative accuracy of this work withrespect to the results of previous studies, in particular, themost recent studies of Silavi et al. (2006) and Amiri et al.(2007) which have been done with the same criteria in thisarea, is computed and the results is shown in Fig. 8.

Both of these two works considered the five class labelsfor seismic vulnerability of Tehran. Figure 8 illustrates theresult of comparison between granular computing classifi-cation approach and the two previous methods. In thiscomparison, each labeled urban areas by granular comput-ing approach is compared to the mutual urban areas whichis labeled by Dempster–Shafer (Amiri et al. 2007) andintuitionistic fuzzy (Silavi et al. 2006) theories.

By the comparison of the result of granular computingclassification approaches with the pessimistic result ofintuitionistic fuzzy approach (column a in the diagram)

Up4=medium

Bet66-88=high

Up4=high

{u4, u9}

{u6, u8}

{u3}Class 3

Class2

Class4

Universe{u1, u2, u3, u4, u5, u6, u7, u8, u9, 10}

Bet66-88=very high

{u7, u5}

{u1, u2, u5 u10}

Up4=very high

Bef66=mediumClass4

{u1, u10}

Class 5

Bef66=high

{u2, u5}

Class4

Fig. 5 The developed granuledecision tree from 10 selectedurban areas in this paper

Appl Geomat (2011) 3:229–240 237

and with the optimistic result of intuitionistic fuzzyapproach (column b in the diagram) also with the result ofDempster–Shafer (column c in the diagram), it can beunderstood that approximately 46% of urban areas of ourresearch have the same seismic vulnerability degree ofDempster–Shafer theory and 44% of urban areas of thisstudy have a one-degree difference.

Conclusion

This paper has proposed a new approach to analyzeclassification of physical vulnerability against earthquakeconsidering the northern fault of Tehran is activated. Someinformation about the effective parameters to vulnerability

in each urban areas in Tehran including earthquakeintensity in terms of MMI unit, slope, weak buildings lessthan four floors, percentage of buildings with more thanfour floors, percentage of buildings built before 1966, andpercentage of buildings built between 1966 and 1988 wereconsidered, to produce Tehran’s seismic vulnerability map.

Also, this paper demonstrates the prominent advantage ofusing granular computing approach in classification. Thismethod infers the classification rules with maximum consis-tency. In addition, contrary to the classical approaches which

Fig. 6 Seismic vulnerabilitymap for 3,173 urban statisticalunits

Fig. 7 Tehran’s urban areas frequency based on seismic vulnerabilitydegree

Fig. 8 The percent of difference between the result of granularcomputing classification approaches and the result of Dempster–Shafer and intuitionistic fuzzy theories (the horizontal axes is thedifference of seismic vulnerability degree of mutual urban areas andthe perpendicular axes shows the percent of urban areas)

238 Appl Geomat (2011) 3:229–240

focus on the selection of a suitable partition, a family ofgranules is defined using the values of an attribute at each stepand the selection of a single granule is considered.

Comparing results between granular computing ap-proach with intuitionistic fuzzy and Dempster–Shafershowed that our results are near to the Dempster–Shafertheory results than to the pessimistic results of intuitionisticfuzzy approach. Generally, results show the expectedseismic vulnerability for Tehran by considering that thenorthern fault of Tehran is activated.

To estimate the impact of other eventually activating faultson the resulting map, it is hereby suggested to evaluate therobustness of this model in the next studies.

Acknowledgement The authors would like to thank associateprof. M. Zare, Associate Professor of Engineering Seismology,and Director of National Center for Earthquake Prediction InternationalInstitute of Earthquake Engineering and Seismology, for constructivediscussions and collaborations on seismic vulnerability assessment. Theauthors would also like to thank Dr. M. Olsen, Assistant Professor ofGeomaticsSchool of Civil and Construction Engineering Oregon StateUniversity for his helpful comments related to our paper.

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