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Fuzzy Measure Theory
Zhenyuan Wang,George J. Klir +1 more
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TLDR
Introduction.Abstract:
Introduction. Required Background in Set Theory. Fuzzy Measures. Extensions. Structural Characteristics for Set Functions. Measurable Functions on Fuzzy Measure Spaces. Fuzzy Integrals. PanIntegrals. Applications. Index.read more
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Journal ArticleDOI
Exhaustivity and absolute continuity of fuzzy measures
TL;DR: This paper further investigates the concept of absolute continuity of fuzzy measures and monotone functions defined by fuzzy integral by using the idea of exhaustivity, and establishes the equivalencies among several different types ofabsolute continuity of warm measures.
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Definite integrals of multiplicative intuitionistic fuzzy information in decision making
TL;DR: The fundamental theorem of calculus is deduced, the forms of indefinite integrals are studied, the concrete formulas for ease of calculating definite integrals from different angles are derived, and some useful properties of the proposed definite integral are discussed.
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Chebyshev type inequalities for general fuzzy integrals
TL;DR: A class of binary operation called g -seminorm is introduced, which generalizes the concept of t -se Minorm and establishes some new Chebyshev type inequalities for this kind of integral.
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Pseudometric generating property and autocontinuity of fuzzy measures
TL;DR: Several necessary and sufficient conditions for the pseudometric generating property of non-additive set functions are given and any uniformly autocontinuous finite fuzzy measure is equivalent to a subadditive finite fuzzy measures.
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Sugeno fuzzy integral for finding fuzzy if–then classification rules
TL;DR: The Sugeno fuzzy integral is used to determine the degrees of importance for individual fuzzy grids that are generated by partitioning each data attribute with various linguistic values; then, fuzzy if–then classification rules are discovered from those fuzzy grids whose degree of importance is larger than or equal to a user-specified minimum threshold.