A Study On Several Types Of Properties Of Fuzzy Integral

In this paper,we will do some research on several properties of fuzzy integrals,the following is our main work which consists of four parts:In Chapter 1,we summarize the development of the fuzzy integral theory,the current research states,the tendency of this topic,and the reason why we choose the topic.The Chapter 2,the definition of the generalized fuzzy integral on a fuzzy set is introduced.After the basic properties of this integral are discussed,some important results,such as the monotone convergence theorem and Fatou lemma,are stablished.Some conditions for integral equations having a solution are also given.In Chapter 3,in terms of fuzzy number order is derived the limit of the sequence of fuzzy numbers.we generalized the integration intervals of fuzzy value functions from bounded closed intervals to infinite intervals,and discussed the elementary properties and integrability conditions for this new kind of integration.In Chapter 4,the(N)-integral of measurable generalized real-valued functions is defined,and its basic properties are discussed.