Multiple Criteria Decision Making with Generalized Fuzzy Sets Arithmetic Operations

Abstract

In this paper, the aggregation of the multiple criteria decision making (MCDM) with linguistic judgments is generalized. The ‘min’ operator in the Zadeh's extension principle for fuzzy arithmetic is replaced with the generalized triangular norms (t-norm). The fuzziness of the fuzzy arithmetic results would be uncontrollable under ‘min’ operator such that the real world applications might not be reliable. The non-flat and subnormal fuzzy numbers are defined and referred to as the generalized fuzzy numbers. The closed form expressions of the fuzzy addition and fuzzy multiplication for generalized fuzzy numbers are developed for various t-norms. The aggregation of the overall fuzzy rates of the alternatives are introduced based on the generalized t-norms. A supplier selection decision making problem is illustrated for the presented approach.