Read e-book online Triangular Norm-Based Measures and Games with Fuzzy PDF

By D. Butnariu,Erich Peter Klement

ISBN-10: 0792323696

ISBN-13: 9780792323693

This booklet goals to provide, in a unified process, a chain of mathematical effects con­ cerning triangular norm-based measures and a category of cooperative video games with Juzzy coalitions. Our procedure intends to stress that triangular norm-based measures are strong instruments in exploring the coalitional behaviour in 'such video games. They now not and simplify a few technical facets of the already classical axiomatic the­ basically unify ory of Aumann-Shapley values, but additionally offer new views and insights into those effects. furthermore, this equipment permits us to acquire, within the video game theoretical context, new and heuristically significant info, which has an important impression on balancedness and equilibria research in a cooperative surroundings. From a proper viewpoint, triangular norm-based measures are valuations on subsets of a unit dice [0, 1]X which shield twin binary operations triggered by way of trian­ gular norms at the unit period [0, 1]. Triangular norms (and their twin conorms) are algebraic operations on [0,1] which have been steered by way of MENGER [1942] and which proved to be helpful within the conception of probabilistic metric areas (see additionally [WALD 1943]). the assumption of a triangular norm-based degree was once implicitly used less than numerous names: vector integrals [DVORETZKY, WALD & WOLFOWITZ 1951], prob­ talents oj Juzzy occasions [ZADEH 1968], and measures on excellent units [AUMANN & SHAPLEY 1974, p. 152].

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Triangular Norm-Based Measures and Games with Fuzzy Coalitions (Theory and Decision Library C) by D. Butnariu,Erich Peter Klement

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