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Fuzzy Optimization and Decision Making

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22-09-2016

Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches

Author: Yu-Hsien Liao

Published in: Fuzzy Optimization and Decision Making | Issue 3/2017

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Abstract

By applying the supreme-utilities under fuzzy behavior, we propose a new solution on fuzzy games. In order to present the rationality for this solution, we adopt an extended reduction to provide related axiomatizations and dynamics process. Based on different viewpoint, we also define excess function to introduce alternative formulation and related dynamic process for this solution respectively.

next article An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations

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A fuzzy TU game, which is defined by Aubin (1974, (1981), is a pair \((N,v^a)\), where N is a coalition and \(v^a\) is a mapping such that \(v^a:[0,1]^N\longrightarrow {\mathbb {R}}\) and \(v^a(0_N)=0\). In fact, \((N,v^a)=(N,\theta ^N,v)\), where for all \(T\subseteq N\), \(\theta ^T \in {\mathbb {R}}^N\) is the vector with \(\theta ^T_i=1\) if \(i\in T\), and \(\theta ^T_i=0\) if \(i\in N{\setminus }T\).

From now on we consider bounded fuzzy TU games, defined as those games (N, b, v) such that, there exists \(K_v\in {\mathbb {R}}\) such that \(v(\alpha ) \le K_v\) for all \(\alpha \in B^N\). We adopt it to ensure that \(v^*(S)\) is well-defined.

For the discussion of x-dependent reduction, please see Maschler and Owen (1989).

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Title: Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches
Author: Yu-Hsien Liao
Publication date: 22-09-2016
Publisher: Springer US
Published in: Fuzzy Optimization and Decision Making / Issue 3/2017
Print ISSN: 1568-4539
Electronic ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-016-9248-6

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