Further Discussion On (Y) Fuzzy Integral And Its Application

Fuzzy measure and fuzzy integral theory is the extence of the classic measure theory. In this paper, we promote (Y) fuzzy integral to the generalized fuzzy measure space in the condition that the integrand is unchanged, learning from non-additive fuzzy measure, set-valued fuzzy measure and fuzzy-valued fuzzy measure.(Y) fuzzy integral’s properties, convergence theorems and application in fuzzy comprehensive evaluation are studied, which based on Lebesgue-Stieltjes measure, set-valued fuzzy measure, and fuzzy-valued fuzzy measure, respectively. It is organized as follows:Part one A new definition of (Y) fuzzy integral is given. Convergence theorem and integral conversion theorem of (Y) fuzzy integral are discussed based on L-S measure, which is in the form of Lebesgue-Stieltjes integral. At the same time, set-valued (Y) fuzzy integral in the form of Lebesgue-Stieltjes integral is defined, incluing its relevant properties and convergence theorems.Part two Set-valued (Y) fuzzy integral is defined, which is based on set-valued fuzzy measure, the relevant properties and convergence theorems are presented.Part three we discuss convergence theorems of fuzzy-valued (Y) fuzzy integral, and prove that the generalized fuzzy integral have some properties when fuzzy integral satisfy some conditions.Part four we introduce the application in fuzzy comprehensive evaluation of (Y) fuzzy integral, combine the fuzzy integral theory with probability.