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Fuzzy Measure Theory
Zhenyuan Wang,George J. Klir +1 more
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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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Book ChapterDOI
2 – From Classical Mathematics to Fuzzy Mathematics: Emergence of a New Paradigm for Theoretical Science
TL;DR: In this article, a major paradigm change that concerns the role of uncertainty in science is discussed, which is manifested by a transition from the traditional attitude toward uncertainty, where uncertainty is undesirable and the ideal is to eliminate it, to an alternative attitude, according to which uncertainty is fundamental and its avoidance is counterproductive.
Journal ArticleDOI
Indistinguishability operators in measurement theory, Part II: Construction of indistinguishability operators based on probability distributions
TL;DR: The main subject of this paper is the problem of constructing indistinguishability operators in terms of probability distribution functions and the probability density functions.
Journal ArticleDOI
On the measure based formulation of multi-criteria decision functions
Ronald R. Yager,Naif Alajlan +1 more
TL;DR: This work looks at various fuzzy measures and investigates the types of decision functions they allow us to formulate and shows how to model linguistically specified decision functions using fuzzy measures.
Journal ArticleDOI
The relationship between structural characteristics of fuzzy measure
Yian-Kui Lui,Boading Liu +1 more
TL;DR: The converse problems of convergence theorems, such as Egoroff's theorem and Riesz's theorem, are discussed and some new results about the relationship between structural characteristics of fuzzy measure and convergences of sequences of measurable functions are obtained.
Journal ArticleDOI
A note on the idempotent functions with respect to pseudo-convolution
TL;DR: A general notion of pseudo-convolution based on pseudo-arithmetical operations is recalled and the idempotents with respect to pseudo-convolutions are investigated.