Comparison of accuracy in ranking alternatives performing generalized fuzzy average functions

Abstract

The paper defines the notions of point, interval and triangular intuitionistic fuzzy numbers expressing the degree of membership and non-membership in the fuzzy set. The generalized fuzzy weighted average function is introduced according to operation rules on intuitionistic fuzzy numbers. In special cases, the generalized weighted average coincides with an arithmetic average or a geometric average. The generalized fuzzy weighted average function could be applied for solving problems in multiple criteria decision making. Research on the stability of the generalized weighted averaging operator of ranking alternatives was performed applying the Monte Carlo method. The aim of the conducted research is to establish the types of intuitionistic fuzzy numbers and the exponent values of the generalized weighted averaging operator having the least error probabilities considering alternatives ranking. Computations were performed involving 3, 4 and 5 experts. In the case of 5 experts, initial decision matrices having high, middle and low separability alternatives were examined. Decision matrices created by the experts were modelled generating random intuitionistic fuzzy numbers according to uniform and normal distribution. The example of applying such methodology was shown to solve a real problem of ranking possible redevelopment alternatives for derelict rural buildings.

Keyword : intuitionistic fuzzy number, generalized weighted averaging operator, multiple criteria decision making, Monte Carlo method