Abstract
In this paper, a max-min solution is proposed based on possibility and necessity measures. This max-min solution is called an "extended max-min solution", since this solution is an extension of the max-min solution previously propoed by Nishizaki et al. A solution algorithm for the Nishizaki's max-min solution, has been proposed only when all components of fuzzy payoff matrices are triangular fuzzy numbers. It is shown that the extended max-min solution can be solved by the similar algorithm even when each component of fuzzy payoff matrices is an arbitrary L-R fuzzy number. Thus, the extended max-min solution can be obtained by the simplex method together with the bisection method. It has been considered that to illustrate the achivements of all fuzzy goals for a solution, n × K figures have been needed, where n is the number of pure strategies and K is the number of fuzzy goals. In this paper, it is shown that only K figures are needed to illustrate the achievements of all fuzzy goals. From this fact, it is easier to recognize all of the achievements of fuzzy goals. Thus, a decision maker can be easily checked whether his/her intended solution is obtained or not. In the last section of this paper, a numerical example is given to exemplify the proposed methods.
