Site selection for temporary housing following earthquake under conditions of uncertainty using classical Fuzzy Logic and Intuitionistic Fuzzy Logic - Case study: District 2 of Tehran Municipality

 Earthquake is one of the most frequent natural hazardsannually leading to numerous human and economic losses. Both in the planning stage and after the earthquake occurrence in the relief phase,findingappropriate sites for temporary housing is considered to be one of the most important issues in reduction of damages caused by earthquake. Temporary housing, especially in a crisis situation is always accompanied by elements of uncertainty. Hence, definitive and classical approaches normally do not lead to acceptable results without involving elements of uncertainty. Although using methods based on fuzzy logic and fuzzy set theory are conventional and appropriate for uncertainty modeling, these methods also have their own disadvantages. For an instance, they require a certain and definitive membership function for each parameter. Moreover,fuzzy theory cannot describe verbal variables related to doubt and hesitation.Temporary housing is always accompanied byuncertainty.Thus, fuzzy theory cannot lead to reliable results in this regard. However, in case sufficient information is not obtained using fuzzy theory, intuitionistic fuzzy logic isconsidered to be an appropriate solution for this problem and uncertaintymodeling. Despite various applications of intuitionistic fuzzy logic in uncertainty modeling, few researches have focused on this method.

Designing a qualitative model based on human knowledge requires a rule-based inference system, which is called an Expert System. This system consists of several parts. In the knowledge-based part, data and a set of rules, which are based on expert knowledgearesavedin the form of logical sentences. The input of this system is a set of numbers fuzzified in the inference engine by a set of fuzzy rules. Then,defuzzification is performed to map the fuzzy set and reach a certain point. In other words, the outputs must be readable and easy for the users.The present study takes advantage of fuzzy and intuitionistic fuzzy approaches todetermine optimal sites for temporary housing. Furthermore, determinant factors of danger and safety followinganearthquakeare used to identify safe places for sheltering in such situations. The present study has applied layers of faults, hospitals, emergency and medical centers, fire stations, parks and green spaces, and roads as determinant factors. New spatial layers were produced for each ofthe aforementioned layers using distance and other similar functions. Then, trapezoidal functionwas used to determine membership and non-membership function of each layer in both fuzzy and intuitionistic fuzzy methods. Membership functions obtained from these methods are different in that they assign different membership values to the pixels surrounding the layer. Following the definition of membership and non-membership functions for each layer in both methods, temporary accommodation maps were obtained using the classical fuzzy as well as intuitionistic fuzzy methods.

The results obtained from these two methods were not identical. The main reason for this difference is that they treat data uncertainty differently. Furthermore, the results of membership and non-membership functions inintuitionistic fuzzy are not complementary. This provides us with a powerful tool for interpretation and, of course, decision making about the study area. As the first case, membership and non-membership degreesequal zero and one implying that the membership degree equals one and the non-membership degree equalszero. This occurs when the method identifies the area as quite appropriate for temporary housing after the earthquake. In this case,results are determinative, and data can be used in the area. In the second case, membership and non-membership degreesare low, which occurs in areas lacking enough information. It implies that more information is neededin such areas for decision making. The third condition takes place when both membership and non-membership degrees equal 0.5. In such a case,it can be conclude that either the stated variable belongs to the area with a membership degree of 0.5, or the variable doesn’t belong to the area with a non-membership degree of 0.5. In the fourth condition, the membership degree is high and the non-membership degree is low. In this case, the results can be trusted and used in decision-making. The fifth condition is in contrast with the fourth case. It occurs when the non-membership degree is high and membership degree is low. Under this condition, it can be concluded that the results are not reliable.

The proposed method and model were implemented in the second district of Tehran. According to the results, it can be concluded that the proposed approachperforms better than theclassical fuzzy approach, especially in the presence ofuncertainvariablesand lack of adequate data.