Multiple Attributes Group Decision Making by Type-2 Fuzzy Sets and Systems

Abstract: We are living in a world full of uncertainty and ambiguity. We usually ask ourselves questions that we are uncertain about their answers. Is it going to rain tomorrow? What will be the exchange rate of euro next month? Why, where and how should I invest? Type-1 Fuzzy sets are characterized by the membership function whose value for a given element x is said to be the grade of membership having a value in the interval [0, 1]. In addition, type-1 fuzzy sets have limited capabilities to deal with uncertainty. In our thesis, we study another concept of a fuzzy description of uncertainty which is called Type-2 fuzzy sets. According to this concept, for any given element x, we can’t speak of an unambiguously specified value of the membership function. Moreover, Type-2 fuzzy sets constitute a powerful tool for handling uncertainty. The aim of our thesis is to examine the potential of the Type-2 fuzzy sets especially in decision making. So, we present basic definitions concerning Type-2 fuzzy sets, and operations on these sets are to be discussed too. Then, Type-2 fuzzy relations and methods of transformation of Type-2 fuzzy sets will be introduced. Also, the theory of Type-2 Fuzzy sets will serve for the construction of the fuzzy inference system. Finally, we utilize interval type-2 fuzzy sets in the application of Multiple Attributes Group Decision Making which is called TOPSIS.