Researches On Single-valued Generalized Fuzzy Integrals Of Set-valued Mappings And Relative Problems

This dissertation investigates the single-valued generalized fuzzy integrals of set-valued mappings and some relative problems.In the first part, it discusses some classical properties and convergence theorems of the single-valued generalized fuzzy integrals of set-valued mappings. First, by introducing the generalized triangle norms, we give the definition of the integral, which is referenced above. Then investigate some basic properties of this kind of integral. Second, a sufficient and necessity condition is given, when two set-valued mappings equal almost everywhere contain their integrals are equal. At last, two important monotone convergence theorems of the integral are given.In the second part, it discusses the condition to solve the single-valued generalized fuzzy integral equation of set-valued mappings.