1990 Volume 2 Issue 1 Pages 65-78
Owing to the complexity of the problems, the objective functions have so fartreated using the information about preferences or aspirations of decision makers in mathematical programming problems with fuzzy coefficients. Namely, it intends to satisfy rather than to optimize. Recently, extending the concepts of optimality and efficiency, a few researchers attempt to optimize the objective functions of fuzzy mathematical programming problems. In this paper, the concepts of efficient solutions or nondominated solutions for usual multiple objective programming probelms are extended for fuzzy multiple objective programming problems in two different manners, which are direct extension manner and the manner based on constructing dominance relation in decision space from the relation in objective space. Using modality measures, i.e., possibility measure and necessity measure, two kinds of efficient solutions are derived from the former manner and six kinds of nondominated solutions from the latter. As the result, we have eight kinds of solutions. In order to arrange these eight solutions, the relationships are investigated. Two of these eight solutions are equivalent to the other two and eight kinds are reduced to six kinds. Moreover, the six kinds of solutions are reduced to four kinds when a usual relation ≧ is adopted for a dominance relation in fuzzy multiple objective linear programming problems with non-interactive fuzzy coefficients. Since these six kinds of solutions are constructed using modality measures, they have linguistic representations, and may play a significant role when we discuss the rationality of the solutions.
