Fuzzy Number Fuzzy Measures and Fuzzy Integrals
نویسندگان
چکیده
By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a function with respect to a fuzzy number fuzzy measure and shown some properties and generalized convergence theorems. It is well-known that a fuzzy-valued function [3,4] is an extension of a function (point-valued), and the fuzzy integral of fuzzy-valued functions with respect fuzzy measures (point-valued) has been studied [3]; so it is natural to ask whether we can establish a theory about fuzzy integrals of fuzzy valued function with respect to fuzzy number fuzzy measures, the answer is just the paper's purpose. The paper is considered as a subsequent one of our earlier paper is considered as a subsequent one of our earlier work in [2]. In fact, it is also a continued work of [3]. Since what we will discuss in the following is a generalization of works in [2, 3]. Throughout the paper, R + will denote the interval[0,∞), X is an arbitrary fixed set,
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