zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Solutions for fuzzy matrix games. (English) Zbl 1201.91003
Summary: We deal with two-person zero-sum games with fuzzy payoffs and fuzzy goals. We present two models for studying two-person zero-sum matrix games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. We obtain that the fuzzy relation approach and the max-min solution are equivalent.
91A052-person games
15B15Fuzzy matrices
[1]Sakawa, M.; Nishizaki, I.: MAX–MIN solutions for fuzzy multiobjective matrix games, Fuzzy sets and systems 67, 53-69 (1994) · Zbl 0844.90117 · doi:10.1016/0165-0114(94)90208-9
[2]Vijay, V.; Mehra, A.; Chandra, S.; Bector, C. R.: Fuzzy matrix games via a fuzzy relation approach, Fuzzy optimization and decision making 6, 299-314 (2007) · Zbl 1151.91319 · doi:10.1007/s10700-007-9015-9
[3]Blackwell, D.: An analog of the minimax theorem for vector payoffs, Pacific journal of mathematics 98, 1-8 (1956) · Zbl 0074.34403
[4]Olivtti, I.; Milano, C.: A decision model under certainty with multiple payoffs, Theory of games; techniques and applications, 50-63 (1966)
[5]Nishizaki, I.; Sakawa, M.: Two-person zero-sum games with multiple fuzzy goals, Journal of Japanese society of fuzzy theory systems 4, 504-511 (1992)
[6]Zeleny, M.: Games with multiple payoffs, International journal of game theory 4, 179-191 (1975) · Zbl 0395.90093 · doi:10.1007/BF01769266
[7]Charnes, A.; Huang, Z.; Rousseau, J.; Wei, Q.: Cone extremal solutions of multi-payoff games with cross-constrained strategy set, Optimization 21, 51-69 (1990) · Zbl 0726.90099 · doi:10.1080/02331939008843519
[8]Zhao, J.: The equilibria of a multiple objective game, International journal of game theory 20, 171-182 (1991) · Zbl 0743.90123 · doi:10.1007/BF01240277
[9]Aubin, J. P.: Mathematical methods of game and economic theory, (1979)
[10]Aubin, J. P.: Cooperative fuzzy game, Mathematics of operations research 6, 1-13 (1981) · Zbl 0496.90092 · doi:10.1287/moor.6.1.1
[11]Butnariu, D.: Fuzzy games: a description of the concept, Fuzzy sets and systems 1, 181-192 (1978) · Zbl 0389.90100 · doi:10.1016/0165-0114(78)90003-9
[12]Butnariu, D.: Stability and Shapley value for n-person fuzzy game, Fuzzy sets and systems 4, 63-72 (1980) · Zbl 0442.90112 · doi:10.1016/0165-0114(80)90064-0
[13]Campos, L.: Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy sets and systems 32, 275-289 (1989) · Zbl 0675.90098 · doi:10.1016/0165-0114(89)90260-1
[14]Nishizaki, I.; Sakawa, M.: Fuzzy and multiobjective games for conflict resolution, (2003)
[15]Bector, C. R.; Chandra, S.: Fuzzy mathematical programming and fuzzy matrix game, (2005)
[16]W. Rodder, H.J. Zimmermann, Duality in fuzzy linear programming, in: A.V. Fiacco, K.O. Kortanek (Eds.), Extremal Methods and System Analysis, Berlin, New York, pp. 415–429.
[17]Bector, C. R.; Chandra, S.: On duality in linear programming under fuzzy environment, Fuzzy sets and systems 125, 317-325 (2000) · Zbl 1014.90117 · doi:10.1016/S0165-0114(00)00122-6
[18]Bector, C. R.; Chandra, S.; Vijay, V.: Matrix games with fuzzy goals and fuzzy linear programming duality, Fuzzy optimization and decision making 3, 263-277 (2004) · Zbl 1079.90183 · doi:10.1023/B:FODM.0000036866.18909.f1
[19]Vijay, V.; Chandra, S.; Bector, C. R.: Matrix games with fuzzy goals and fuzzy payoffs, Omega: the international journal of management 33, 425-429 (2005)
[20]Wu, H. C.: Duality theory in fuzzy linear programming problems with fuzzy coefficients, Fuzzy optimization and decision making 2, 61-73 (2003)
[21]Inuiguchi, M.; Ramik, J.; Tanino, T.; Vlach, M.: Satisficing solutions and duality in interval and fuzzy linear programming, Fuzzy sets and systems 135, 151-177 (2003) · Zbl 1026.90105 · doi:10.1016/S0165-0114(02)00253-1
[22]Ramik, J.: Duality in fuzzy linear programming: some new concepts and results, Fuzzy optimization and decision making 4, 25-39 (2005) · Zbl 1079.90184 · doi:10.1007/s10700-004-5568-z
[23]Ramik, J.: Duality in fuzzy linear programming with possibility and necessity relations, Fuzzy sets and systems 157, 1283-1302 (2006) · Zbl 1132.90385 · doi:10.1016/j.fss.2005.11.022
[24]Owen, G.: Game theory, (1995)
[25]Nishizaki, I.; Sakawa, M.: Equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals, Journal of optimization theory and applications 86, 433-457 (1995) · Zbl 0838.90145 · doi:10.1007/BF02192089
[26]Bellman, R. E.; Zadeh, L. A.: Decision making in a fuzzy environment, Management sciences 17, 209-215 (1970) · Zbl 0224.90032
[27]Nishizaki, I.; Sakawa, M.: Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals, Fuzzy sets and systems 111, 99-116 (2000) · Zbl 0944.91001 · doi:10.1016/S0165-0114(98)00455-2
[28]Shimizu, K.; Aiyoshi, E.: Neccesary conditions for MIN–MAX problems and algorithm by a relaxation procedure, IEEE transactions on automatic control 25, 62-66 (1980) · Zbl 0426.49008 · doi:10.1109/TAC.1980.1102226
[29]Sakawa, M.: Interactive computer program for fuzzy linear programming with multiple objectives, International journal of man-machine studies 18, 489-503 (1983) · Zbl 0513.90079 · doi:10.1016/S0020-7373(83)80022-4
[30]Charnes, A.; Cooper, W.: Programming with linear fractional function, Naval research logistics quarterly 9, 181-186 (1962) · Zbl 0127.36901 · doi:10.1002/nav.3800090303
[31]Zimmermann, H. J.: Fuzzy sets theory and its applications, (2006)
[32]Dubois, D.; Prade, H.: Ranking fuzzy numbers in the setting of possibility theory, Information sciences 30, 183-224 (1983) · Zbl 0569.94031 · doi:10.1016/0020-0255(83)90025-7
[33]Inuiguchi, M.; Ichihashi, H.; Kume, Y.: Modality constrained problems: a unified approach to fuzzy mathematical programming problems in the setting of possibility theory, Information sciences 67, 93-126 (1993) · Zbl 0770.90078 · doi:10.1016/0020-0255(93)90086-2
[34]Kaufmann, A.; Gupta, M. M.: Introduction to fuzzy arithmetic, theory and applications, (1991) · Zbl 0754.26012