An interactive fuzzy satisficing method for multiobjective linear fractional programming problems

The authors present a new interactive fuzzy decision making method for solving multiobjective linear fractional programming problems by assuming that the decision maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions including nonlinear functions. After determining the membership functions, if the DM specifies reference membership values, the minimax problem is solved by combined use of the bisection method and the linear programming method, and the DM is supplied with the corresponding Pareto optimal solution together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his/her reference membership values. In this way, the compromise or satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his/her reference membership values. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs.