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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
Citations
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Bellman's optimality principle in the weakly structurable dynamic systems
Gia Sirbiladze,Anna Sikharulidze +1 more
TL;DR: Sufficient and necessary conditions are presented for the existence of an extremal fuzzy optimal control processes, for which R. Bellman's optimality principle and take into consideration the gain-loss fuzzy process are used.
Proceedings ArticleDOI
Extension of the Sugeno Integral with Interval Type-2 Fuzzy Logic
Olivia Mendoza,Patricia Melin +1 more
TL;DR: The generalization includes modifying the original equations of the Sugeno Measures and Sugeno Integral to enable calculation of the interval Type-2 SugenoIntegral for combining multiple source of information.
Book ChapterDOI
Extension of Lower Probabilities and Coherence of Belief Measures
Zhenyuan Wang,Wei Wang +1 more
TL;DR: Using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions and are established that all belief measures are coherent imprecise probabilities.
Book ChapterDOI
Advances in the Egalitarist Approach to Decision-Making in a Fuzzy Environment
Didier Dubois,Henri Prade +1 more
TL;DR: This paper proposes a unified approach to decision-making in a fuzzy environment, based on the original idea of Bellman and Zadeh, encompassing fuzzy optimization, fuzzy relational calculus and possibility theory, which subsumes the paradigm of constraint-directed reasoning in Artificial Intelligence and allows for flexible or prioritized constraints.
Journal ArticleDOI
Evaluating Choquet Integrals Whose Arguments are Probability Distributions
TL;DR: The use of the Choquet integral for finding a mean-like aggregated value of a collection of arguments with respect to a fuzzy measure is described and one surrogate for calculating this integral is provided in the case where the objects being aggregated are probability distributions called the probabilistic exceedance method.