A unified method of defuzzification for type-2 fuzzy numbers with its application to multiobjective decision making

Abstract

This paper introduces a process of defuzzification for ranking of type-2 trapezoidal fuzzy numbers. A two-phase defuzzification method has been developed using probability density function of the random variables associated with the fuzzy numbers. This method finds an equivalent defuzzified value of type-2 fuzzy numbers through phasewise reduction. The process reduces the computational complexities for using type-2 fuzzy numbers significantly and it is applicable to not only type-2 fuzzy numbers but also to any types of fuzzy numbers for ranking them properly. To illustrate the proposed defuzzification process, the method is applied on a set of type-2 trapezoidal fuzzy numbers and ranked them according to their defuzzified values. The achieved results are compared with other existing ranking methods. Furthermore, a multiobjective linear programming model having type-2 fuzzy numbers as parameters is solved using the proposed defuzzification process. Fuzzy goal programming technique is used for achieving the highest degree of each of the defined membership goals to the extent possible in the decision-making context. A numerical example is provided to demonstrate the efficiency of the proposed methodology.