The Generalization Of K-quasi-additive Fuzzy Integral

The research on quasi-additive fuzzy measure and quasi-additive fuzzy integral has made great progress, which has formed an important branch of fuzzy mathematics. Especially, its application in the treatment of the things of the uncertainty mathematical tool is more and more widely used in many fields. K-quasi-additive fuzzy measure and integral are proposed, based on quasi-additive fuzzy measure and integral, and K-quasi-additive fuzzy integral is also a kind of K-quasi-additive fuzzy measure. According to definition of K-quasi-additive fuzzy integral and integral conversion theorem, this article provides some new properties, based on the original properties of K-quasi-additive fuzzy measure and integral.This paper mainly includes the following contents:Part I:I simple introduce the background of K-quasi-additive fuzzy integral and the present situation of the study at home and abroad.Part II:I introduce some basic concepts, K-quasi-addition> K-quasi-multiplication、K-quasi-subtracU the definition of bounded fuzzy value function and some important concepts of this paper-K-quasi-additive fuzzy measure space on classic set and fuzzy set、K-quasi-additive fuzzy integral and the definition of related integral transformation theorem.Part III:I give some new properties of K-quasi-additive fuzzy integral on classic set and fuzzy set, and futher perfect the property of K-quasi-additive fuzzy integral.Part IV:I introduce the definition and property of K-quasi-additive fuzzy number valued integral, integral transformation theorem, and give this integral some other forms of the original structure characteristics.Part V:I introduce the definition and property of the dual K-quasi-additive fuzzy number valued integral, integral transformation theorem, and give the decision theorem of the dual K-quasi-additive fuzzy number valued integral. Finally I give an example to illustrate the practical application of this integral in production forecast.