Uncertainty Management using Interval Mathematics and Granular Computing in Seismic Vulnerability Assessment

Earthquake as the most devastating natural disaster in urban areas causes huge physical and human damages worldwide. One way to assist reducing the impact of the earthquake on people and infrastructures is to produce a reliable seismic vulnerability map. The physical seismic vulnerability of a region as a multi criteria problem is concerned with seismic intensity, land slope, the number of building floors, building age and quality. Among the most important sources of uncertainty in determining the vulnerability of each urban statistical unit, is the uncertainty related to the conflicts in expert opinions concerning the level of severity of the seismic vulnerability. The main objective of this paper is to manage uncertainty considering different vulnerability classes allocated by the experts in integration of the concerned parameters. In this model, to reduce the uncertainty in the decision making process related to the expert opinions on allocating a seismic physical vulnerability class to each urban statistical unit, interval mathematics, genetic algorithm and granular computing methods are used. The physical seismic vulnerability map has been produced for Tehran on the basis of activation of North Tehran fault. Among 3174 urban statistical units, 150 randomly selected samples have been selected by 5 experts in related geoscience fields. The experts are asked to fill a questionnaire for allocating the physical seismic vulnerability of the samples. Due to the disaggregation in the experts’ knowledge on the physical seismic vulnerability of each statistical unit, their opinions have been integrated using interval mathematics. For the conflict resolution among the experts, genetic algorithm is used. Granular computing has been applied to manage the uncertainty caused by the large amount of information achieved from the parameters affecting the physical vulnerability to assess the seismic physical vulnerability. The relations among the input parameters and the vulnerability classes are presented in a decision table. The rules with a minimum conflict from the decision table are extracted. The vulnerability classes have been sorted from 1 to 5 considering 1 as the least vulnerable class and 5 as the most vulnerable class. According to the results, most of the statistical units in Tehran fall within interval class vulnerabilities of [3 4] and [5 4]. To compare the similarity between the results of the model and those of the previous research by Khamespnah in the same study area, who used an integrated model of granular computing and rough set theory, Spearman rank correlation coefficient was employed. The value of this coefficient was 0.47 that shows some similarities between the results. The accuracy of 76% was achieved in this research using Kappa index verifying the importance of managing uncertainty using interval mathematics.