Research Of Fuzzy-valued Integral Theory

Motivated by the applications in several areas of applied science,such as mathematical economics,fuzzy optimal,process control and decision theory,much effort has been devoted to generalize classical measure and integral results to the case of fuzzy environment,and relevant knowledge of fuzzy measure and integral has been obtained and applied to actual production and life.In this paper,we also devote ourselves to this work.Our work is divided into two parts:(1)The Pettis type weak integral of a real valued function with respect to set valued measures in Banach spaces,which is introduced by Zhou and Shi,is generalized to the generalized fuzzy number measures.We obtain the Kluv(?)nek-Lewis integral concept of real-valued functions with respect to generalized fuzzy number measures and discuss some properties and convergence theorems.(2)Based on a fuzzy number measure of Zhou,a fuzzy integral of a new real-valued functions with respect to that fuzzy number measure is introduced,and some properties of it are discussed,its convergence theorems is given.