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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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Aggregation Operators of Interval-Valued 2-Tuple Linguistic Information
Ismat Beg,Tabasam Rashid +1 more
TL;DR: A multiple attribute decision‐making method based on new aggregation operators introduced by using the Choquet integral to illustrate the efficiency, practicality, and feasibility of this method.
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Modelling of extremal fuzzy dynamic systems: Part V. Optimization of continuous controllable extremal fuzzy processes and the choice of decisions
TL;DR: Applying Bellman's optimality principle and assuming that the gain–loss process exists for an EFDS, a variant of the fuzzy integral representation of an optimal control is given for continuous EFDSs.
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On the comonotonic-⋆-property for Sugeno integral
Yao Ouyang,Radko Mesiar,Jun Li +2 more
TL;DR: It is proved that Sugeno integral possesses comonotonic-*-property if and only if * equals to one of the four operators: minimum, maximum, PF (the first projection) and PL (the last projection).
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Inconsistency and non-additive capacities: The Analytic Hierarchy Process in the framework of Choquet integration
TL;DR: In this model a measure of dominance inconsistency between criteria is defined in terms of the totally inconsistent matrix associated with the main pairwise comparison matrix of the AHP to construct a non-additive capacity whose associated Shapley values reduce to the standard AHP priority weights in the consistency case.
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A further investigation for fuzzy measures on metric spaces
TL;DR: The aim of this paper is to prove the Egoroff's theorem and Lusin's theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric generating property.