An interactive fuzzy satisficing method using augmented minimax problems and its application to environmental systems

A new interactive fuzzy satisficing method for multiobjective nonlinear programming is presented, by considering that the decisionmaker (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 corresponding membership functions. In order to generate a candidate for the satisficing solution (Pareto optimal) after determining the membership functions, if the DM specifies his / her reference membership values, the augmented minimax problem is solved. The DM is thus 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 acts on this solution by updating his / her reference membership values. In this way the 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 to implement man-machine interactive procedures. An application to the industrial pollution control problem in Osaka City in Japan is demonstrated together with the computer output.