An Interactive Fuzzy Decisionmaking Method Using Constraint Problems

Abstract
An interactive fuzzy decisionmaking method is presented, which assumes that the decisionmaker (DM) has fuzzy goals for each of the objective functions in multiobjective nonlinear programming problems. Having determined the membership functions for each of the objective functions, if the DM selects an appropriate standing membership function and specifies his/her aspiration levels of achievement of the other membership functions, called constraint membership values, the corresponding constraint problem is solved, and the DM is supplied with the 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 constraint membership values. In this way, the satisficing or compromise solution for the DM can be derived efficiently from among a Pareto optimal solution set. 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 output.