The Research Of Meausable Functions Sequence And (Y) Fuzzy Integral About The Convergence Properties

Fuzzy measure and fuzzy integral theory is an extension of the classical measure theory, the convergence problem of measurable function sequence in fuzzy measure space and fuzzy integral is always a core problem. In this paper, we will focus on the convergence properties for the Measurable function sequence and (Y) fuzzy integral, besides do the further research. According the new definition of "finite null additive", we do the further research and improvement with measurable function sequence. In addition to, we make detailed research with the convergence properties for (Y) fuzzy integral sequences, so as to perfect the fuzzy integral theory knowledge further. In the paper, the main research work includes four aspects as follow:Part Ⅰ:We first introduce the basic knowledge of fuzzy mathematics theory, basic concept of fuzzy measure and some important properties are introduced mainly. We do the compare with the classical measure, the subadditivity is very important in the fuzzy measure theory, which is a core part of fuzzy mathematics.Part Ⅱ:Because the convergence of measure function sequence is very important in the fuzzy measure space, we give kinds of definition about the convergence, and do some research about the relationship for the convergence of measurable function in fuzzy measure space.Part Ⅲ:We introduce a new definition named finite null-subtractivity in the fuzzy measure, and discuss the convergence of measure function sequence further. Besides, we make some improvement for the important convergence theorem such as the lebesgue theorem.Part Ⅳ:On the basis of (Y) fuzzy integral defined by Wenshuang Yu, we add to new basic properties for (Y) fuzzy integral. Besides we do some further research about the (Y) fuzzy integral combining with the convergence theorem of the Choquet integral.