Ｒesearch on Generalized Sugeno Fuzzy Probability Integral Based on t-Modular Operator

Abstract

Fuzzy probability integral is an important part of fuzzy mathematics，and it is an integral form which combines fuzzy probability with integral. In this paper，a quasi-multiplication operator and a quasi-sum operator are designed by using the definition conditions of t-triangular module and s-triangular module. A new credible measure is constructed. The Sugeno fuzzy probability integral is redefined by combining the quasi-multiplication operator in the trusted measure space. According to the new definition of Sugeno fuzzy probability integral，the corresponding linear and nonlinear properties of the integral are obtained，giving the corresponding proof. All these provide the basis for the enrichment and development of Sugeno fuzzy probability integral theory.

Keywords

• t-triangular module
• s-triangular module
• quasi-multiplication operator
• quasisum operator
• trusted measure
• sugen fuzzy probability integral