An Interactive Fuzzy Satisficing Method for Multiobjective Linear-Programming Problems and Its Application

A new interactive fuzzy satisficing method is presented for solving multiobjective linear-programming problems by assuming 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 the corresponding membership functions, including nonlinear functions. After determining the membership functions to generate a candidate for the satisficing solution which is also Pareto optimal, if the DM specifies reference membership values, the minimax problem is solved by combined use of the bisection and linear-programming methods, 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 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 application to an optimal operation problem in a package system in automated warehouses is demonstrated along with the computer outputs.