The Henstock Integral Of Fuzzy-number-valued Functions Over A Directed Line, Convergence Theorems And Its Applications

In order to meet the study needs of the theory of fuzzy integrals and problems of multi-classifier fusion,the integral of fuzzy-number-valued functions is becoming the focus of fuzzy analysis.Firstly,the concept of the Henstock integral of fuzzy-number-valued functions over a directed line is proposed in this paper,the properties of this integral are discussed by means of the Henstock integral of interval-valued functions,vector-valued functions and real-valued functions.In addition,the integrability of the fuzzy derivative function over the fuzzy line is discussed and the Newton-Leibniz fromula is obtained.Secondly,the concept of weak equi-integrability of the sequence of fuzzy-number-valued functions is proposed,and a necessary and sufficient condition of the Henstock integral for the limit function of the sequence of fuzzy-number-valued functions is obtained.Finally,the Choquet integral of fuzzy-number-valued functions based on fuzzy measures and finite universe is presented.It is a special case of the sum of the Henstock integral of a real-number-valued function on direcred line segments.As a application,the multi-classifier fusion is discussed by the Choquet integral proposed in this thesis,and an illustration given shows that the proposed fusion scheme is reasonable and effective.