Fuzzy number fuzzy measures and fuzzy integrals. (I). Fuzzy integrals of functions with respect to fuzzy number fuzzy measures

This paper, based on the fuzzy measures and fuzzy integrals given by Sugeno, first defines interval number fuzzy measures (INF-measures) and fuzzy number fuzzy measures (FNF-measures), and the fuzzy integral of function with respect to INF-measures are given. Then it defines the fuzzy integral of functions with respect to FNF-measures, and the properties and convergence theorems are obtained. All these are generalizations of Sugeno's works.