Journal ArticleDOI
Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals
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This paper considers equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and introduces fuzzy goals for payoffs in order to incorporate ambiguity of a player's judgements and assume that the player tries to maximize degrees of attainment of the fuzzy goals.About:
This article is published in Fuzzy Sets and Systems.The article was published on 2000-04-01. It has received 90 citations till now. The article focuses on the topics: Fuzzy number & Fuzzy set operations.read more
Citations
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Journal ArticleDOI
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers
TL;DR: A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models.
Journal ArticleDOI
Uncertain Shapley value of coalitional game with application to supply chain alliance
Jinwu Gao,Xiangfeng Yang,Di Liu +2 more
TL;DR: Two definitions of uncertain Shapley value are presented: expected ShapleyValue and α-optimistic Shapleyvalue, which are used to solve the profit allocation problem of supply chain alliance and some characterizations of the uncertain Shapleys value are investigated.
Journal ArticleDOI
Linear programming approach to solve interval-valued matrix games
TL;DR: It is proven that two players have the identical interval-type value of the interval-valued matrix game and that the linear programming models and method proposed in this paper extend those of the classical matrix games.
Journal ArticleDOI
A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers
TL;DR: The aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers (TFNs) which always assures that players’ gain-floor and loss-ceiling have a common TFN-type fuzzy value and hereby any matrix game with payoff of TFNs has aTFN- type fuzzy value.
Journal ArticleDOI
Uncertain bimatrix game with applications
TL;DR: This paper introduces a concept of uncertain bimatrix game within the framework of uncertainty theory, and three solution concepts of uncertain equilibrium strategies as well as their existence theorem are proposed.
References
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Book
Decision-making in a fuzzy environment
Richard Bellman,Lotfi A. Zadeh +1 more
TL;DR: A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
Journal ArticleDOI
Bimatrix Equilibrium Points and Mathematical Programming
TL;DR: In this paper, simple constructive proofs are given of solutions to the matric matric system Mz − ω = q; z ≧ 0; ω ≧ 1; zT = 0, for various kinds of data M, q, which embrace quadratic programming and the problem of finding equilibrium points of bimatrix games.
Journal ArticleDOI
Fuzzy linear programming models to solve fuzzy matrix games
TL;DR: A zero-sum two-person game with imprecise values in its matrix of payoffs is considered and a method for its solution based on the establishment of a Fuzzy Linear Programming problem for each player is proposed.
Journal ArticleDOI
Two-person nonzero-sum games and quadratic programming
Olvi L. Mangasarian,H Stone +1 more
TL;DR: In this paper, it was shown that a necessary and sufficient condition that a point be a Nash equilibrium point of a two-person, nonzero-sum game with a finite number of pure strategies is that the point is a solution of a single programming problem with linear constraints and a quadratic objective function that has a global maximum of zero.
Journal ArticleDOI
Max-min solutions for fuzzy multiobjective matrix games
TL;DR: The formulated mathematical programming problem which yields the max-min strategy can be reduced to the linear programming problem by making use of Sakawa's method, the variable transformations, and the relaxation procedure.