Fuzzy linear programming models to solve fuzzy matrix games
Fuzzy Sets and Systems
Computational economics and finance: modeling and analysis with Mathematica
Computational economics and finance: modeling and analysis with Mathematica
Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals
Fuzzy Sets and Systems - Fuzzy mathematical programming
Convex Optimization
Bi-matrix Games with Fuzzy Goals and Fuzzy
Fuzzy Optimization and Decision Making
A First Course in Fuzzy Logic, Third Edition
A First Course in Fuzzy Logic, Third Edition
Fuzzy Mathematical Programming and Fuzzy Matrix Games (Studies in Fuzziness and Soft Computing)
Fuzzy Mathematical Programming and Fuzzy Matrix Games (Studies in Fuzziness and Soft Computing)
Fuzzy and Multiobjective Games for Conflict Resolution (Studies in Fuzziness and Soft Computing)
Fuzzy and Multiobjective Games for Conflict Resolution (Studies in Fuzziness and Soft Computing)
Solving bimatrix games with fuzzy payoffs by introducing Nature as a third player
Fuzzy Sets and Systems
Fuzzy multiobjective optimization modeling with mathematica
WSEAS TRANSACTIONS on SYSTEMS
Two-person zero-sum game approach for fuzzy multiple attribute decision making problems
Fuzzy Sets and Systems
| Hi-index | 0.00 |
This paper introduces to the computational techniques of non-cooperative bimatrix games in an uncertain environment. Both single and multiple objective fuzzy-valued bimatrix games are considered theoretically with one numerical example. The presentation is centered on the Nishizaki and Sakawa models. These models are based on the maxmin and minmax principles of the classical matrix game theory. Equivalent nonlinear (possibly quadratic) programming problems are giving optimal solutions. The equilibrium solutions correspond to players maximizing a degree of attainment of the fuzzy goals. Besides the Nash equilibrium, the concept of α-Nash equilibrium supposes Nature be the third Player. The aggregation of all the fuzzy sets in the multiobjective models use the fuzzy decision rule by Bellman and Zadeh. This 'aggregation by a minimum component' consists in the intersection of the fuzzy sets, the fuzzy expected payoffs and the fuzzy goals. Numerical examples of two-players nonzero sum games are solved using the MATHEMATICA 7.0.1 software. The numerical solutions are possibly local by using iterative methods.