The generalized expectations of the reductions for type-2 fuzzy variable

Abstract

In fuzzy possibility theory, type-2 (T2) fuzzy variable is an appropriate tool for describing T2 fuzziness. T2 triangular fuzzy variable is one common T2 fuzzy variable. Based on the concepts of generalized credibility and generalized expectation, this paper deduces the generalized expectation formulas for the three reductions of T2 triangular fuzzy variable which are obtained by using the critical value (CV) reduction methods. While solving some optimization problems with T2 fuzzy coefficients, these formulas will be useful.