Pareto-optimal security strategies in matrix games with fuzzy payoffs

On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations

“…Let PLFG denote the two person zero-sum fuzzy matrix game with pay-offs of piecewise linear fuzzy numbers. Now following the notations, terminology and results of Clemente et al (Clemente et al, 2011), it can be shown that solving PLFG is equivalent to solving following two multiobjective programming problems (VP) 1 Max v j α i , (i = 1, 2, . .…”

“…150.08, 152.69, 152.91, 156.39, 161.13, 163.58, 164.24, 166.39) 2 (150.22, 152.82, 153.05, 156.53, 161.27, 163.71, 164.38, 166.35) 3 (150.59, 152.18, 153.42, 156.87, 161.62, 164.06, 164.26, 166.22) 4 (150.65, 155.19, 155.47, 158.82, 163.59, 163.41, 163.60, 165. 155.21, 158.48, 159.11, 161.25, 166.04, 167.85, 168.34, 171.25) 2 (155.26, 158.53, 159.16, 161.05, 165.84, 167.66, 168.14, 171.05) 3 (155.61, 158.88, 159.01, 161.63, 166.43, 168.23, 168.72, 171.63) 4 (155.88, 159.11, 159.75, 161.65, 163.59, 165.44, 165.92, 168.82) Remark 5.1. In literature, only matrix games with pay-offs of triangular or trapezoidal fuzzy numbers have been studied, e.g., Li and Yang (Li and Yang, 2004), Bector et al (Bector et al, 2004), Campos (Campos, 1989) and Clemente et al (Clemente et al, 2011). In Bector et al (Bector et al, 2004) and Campos (Campos, 1989) in (VP) 1 and (VP) 2 , leading to more computational effort.…”

“…We also suggest appropriate modifications to take care of this omission. These modifications in conjunction with the results of Clemente et al (Clemente et al, 2011) lead to an algorithm to solve matrix games with pay-offs of general piecewise linear fuzzy numbers.…”

Short rational generating functions for solving some families of fuzzy integer programming problems

“…A possible strategy is to double the number of points by using k = 2 s and by moving automatically to k = 2 s+1 if a better precision is necessary.) However, in the most standard models (see [54][55][56]) a finite and pre-specified ranking system describes exactly the fuzzy numbers. For instance, trapezoidal fuzzy numbers (including triangular fuzzy numbers as a special case) are totally characterized by two elements in the ranking system {α 0 , 1}.…”

Ambiguous games played by players with ambiguity aversion and minimax regret

“…It is assumed in such a model that for each player the consequence or payoff of a strategy profile is determinate or precise. However, this assumption about a strategic game seems implausible when ambiguity is present [4,21,35], since for some strategy profiles a player may not be able to determine their precise payoffs due to limited information.…”