Buradasınız

Anasayfa » Content

A Linear Interactive Solution Concept for Fuzzy Multiobjective Games

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2010

Key Words:

Author NameUniversity of AuthorFaculty of Author

AMS Codes:

Abstract (2. Language): 
In this paper, we deal with multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals. The aim of the paper is to explain new concepts of solutions for multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. A degree of attainment of the fuzzy goal is defined and the max-min strategy with respect to the degree of attainment of the fuzzy goal is examined. If all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear, the max-min solution is formulated as a nonlinear programming problem. The problem can be reduced to a linear programming problem by making use of Sakawa’s method, the variable transformation by Charnes and Cooper and the relaxation procedure.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon arastirmax-linear-interactive-solution-concept-fuzzy-multiobjective-games.pdf
  • 1
107-117
  • English

REFERENCES

References: 

[1] J.P. Aubin, Mathematical Methods of Game and Economic Theory (North-
Holland,Amsterdam,1979).
[2] J.P. Aubin, Cooperative fuzzy game, Math. of Oper. Res. 6 (1981) 1-13.
[3] E.B. Bajalinov, Linear -Fractional Programming Theory, Methods, Applications and Software,
[4] R.E.Bellman and L.A. Zadeh, Decision making in a fuzzy environment, Manag. Sci. 17
(1970) 209-215.
[5] D.Blackwell, An analog of the minimax theorem for vector payoffs, Pacific J. Math. 98
(1956) 1-8.
[6] D.Butnariu, Fuzzy games: A description of the concept, Fuzzy Sets and Systems 1 (1978)
181-192.
[7] D.Butnariu, Stability and shapley value for n-person fuzzy game, Fuzzy Sets and Systems
4 (1980) 63-72.
[8] L.Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets
and Systems 32 (1989) 275-289.
[9] A.Charnes and W. Cooper, Programming with linear fractional function, Naval Res. Logist.
Quart. 9 (1962) 181-186.
[10] A.Charnes, Z.Huang, J.Rousseau and Q. Wei, Cone extremal solutions of multi-payoff
games with cross-constrained strategy set, Optimization 21 (1990) 51-69.
[11] I. Olivtti and C. Milano, A decision model under certainty with multiple payoffs, in: A.
Mensch, Ed., Theory of games; Techniques and Applications (American Elsevier,New
York,1966) 50-63.
[12] W.D. Cook, Zero-sum games with multiple goals, Naval Res. Logist. Quart. 23 (1976)
615-622
[13] I. Nishizaki and M.Sakawa, Two-person zero-sum games with multiple fuzzy goals, J.
Japan Soc. Fuzzy Theory Systems 4 (1992) 504-511.
[14] I. Nishizaki and M.Sakawa, Fuzzy and Multiobjective Games for Conflict Resolution,
Kluwer Academic Publishers 2003.
[15] I. Nishizaki and M.Sakawa, Equilibrium Solutions for Multiobjective Bimatrix Games
Incorporating Fuzzy Goals, Journal of Optimization Theory and Applications, 86 (1995)
433-457.
[16] I. Nishizaki andM.Sakawa, Equilibrium Solutions in Multiobjective Bimatrix Games with
Fuzzy Payoffs and Fuzzy Goals, Fuzzy Sets and Systems, 111 (2000) 99-116.
[17] M.Sakawa and I. Nishizaki, Max-min solutions for fuzzy multiobjective matrix games,
Fuzzy Sets and Systems, 67 (1994) 53-69.
[18] M.Sakawa, Interactive computer program for fuzzy linear programming with multiple
objectives, Int. J. Man-Machine Studies, 18 (1983) 489-503.
[19] K.Shimizu and E.Aiyoshi, Neccesary conditions for min-max problems and algorithm by
a relaxation procedure, IEEE Trans. Automat. Control AC-25 (1980) 62-66.
[20] M.Zeleny, Games with multiple payoffs, Int. J. Game Theory 4 (1975) 179-191.
[21] J.Zhao, The equilibria of a multiple objective game, Int. J. Game Theory 20 (1991)
171-182.

Thank you for copying data from http://www.arastirmax.com