Extensions of Fuzzy Relations Considering Interaction Between Possibility Distributions and an Application to Fuzzy Linear Program

Abstract

In this paper, a controversial point of previous definition of optimal or efficient solutions to mathematical programming problems with fuzzy objective functions is pointed out. As basis for settling the controversial point, the extension methods of fuzzy relations to the relations between interactive or dependent possibility distributions are proposed. Some properties of the extended fuzzy relations are investigated. Next, in order to illustrate the controversial point, a defect of a previous definition of optimal solutions, i. e., α-possibly efficient solutions is clarified and the definition is modified using one of proposed extended fuzzy relations. It is shown that the defect is dissolved by the modified definition.