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Studying interval valued matrix games with fuzzy logic. (English) Zbl 1152.91312
Summary: Matrix games have been widely used in decision making systems. In practice, for the same strategies players take, the corresponding payoffs may be within certain ranges rather than exact values. To model such uncertainty in matrix games, we consider interval-valued game matrices in this paper; and extend the results of classical strictly determined matrix games to fuzzily determined interval matrix games. Finally, we give an initial investigation into mixed strategies for such games.

MSC:
91A06 \(n\)-person games, \(n>2\)
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[1] Allen JF (1983) Maintaining knowledge about temporal intervals. Commun ACM 26:832–843 · Zbl 0519.68079 · doi:10.1145/182.358434
[2] Dutta P (1999) Strategies and games: theory and practice. MIT Press, Cambridge
[3] de Korvin A, Hu C, Sirisaengtaksin O (2000) On firing rules of fuzzy sets of type II. Appl Math 3(2):151–159 · Zbl 1089.68646
[4] Fishburn PC (1985) Interval orders and interval graphs: a study of partially ordered sets. Wiley, New York · Zbl 0551.06001
[5] Fuller R, Zimmermann H (1993) Fuzzy reasoning for solving fuzzy mathematical programming problems. Fuzzy Sets Syst 60:121–133 · Zbl 0795.90086 · doi:10.1016/0165-0114(93)90341-E
[6] Garagic D, Cruz JB (2003) An approach to fuzzy noncooperative Nash games. Optim Theory Appl 118(3):475–491 · Zbl 1073.91002 · doi:10.1023/B:JOTA.0000004867.66302.16
[7] Nash J (1950) Equilibrium points in N-person games. Proc Natl Acad Sci USA 36(1):48–49 · Zbl 0036.01104 · doi:10.1073/pnas.36.1.48
[8] Nash J (1951) Non-cooperative games. Ann Math 54(2):286–295 · Zbl 0045.08202 · doi:10.2307/1969529
[9] Russell S, Lodwick WA (2002) Fuzzy game theory and Internet commerce: e-strategy and metarationality, NAFIPS 2002–proceedings
[10] Winston W (2004) Operations research–applications and algorithms. Brooks-Cole, Belmont · Zbl 0672.90082
[11] Wu S, Soo V (1998) A fuzzy game theoretic approach to multi-agent coordination. LNCS 1599, pp 76–87
[12] Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353 · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
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