Result: Solution concepts for fuzzy multiobjective programming problems
Further Information
Summary: Traditionally, because of the complexity of mathematical programming problems with fuzzy parameters, objective functions were handled by elicitation of the preference structure or the aspiration level from the decision-maker, so that satisfaction rather than optimization was employed. In recent years, even for fuzzy mathematical programming problems, objective functions have been handled by extending the concepts of optimality and efficiency for optimization studies. In the present paper, the concepts of efficient solutions or nondominated solutions to ordinary multiobjective programming problems are approached in two ways. One intends to extend the concepts of efficient solutions directly and the other intends to extend the concepts of nondominated solutions via constructing a domination relation. Using two modality (possibility and necessity) measures, eight types of solution concepts are obtained in total (two in the former approach and six in the latter). To organize these eight types of solutions, their strength and weakness relations are discussed. As a result, these solutions are generally subdivided into six types. In the case of multiobjective linear programming problems, with noninteractie fuzzy parameters, they definitely belong to one of four types if the domination relation is the ordinary inequality relation \(\geq\). As these solutions are defined by using modality measures, the solutions have their own linguistic expressions and are important when discussing the validity of solutions to fuzzy multiobjective programming problems.