An interactive method for multi-goal programming with fuzzy solution using fuzzy reasoning and its application to diet problem

This paper presents a new interactive method for solving fuzzy mathematical programming problems. An interactive method is generally an effective method for obtaining a satisfactory solution, but in many conventional methods, it is difficult to proceed with the process of interaction without having some knowledge of mathematical programming and the understanding of individual methods. In this study the burden of a decision maker during the interactive process is reduced by applying fuzzy reasoning to the problems. Furthermore, a new method that does not require the prior understanding of the method is proposed. The authors apply this interactive method to the fuzzy mathematical programming problem involving both fuzzy decision variables and fuzzy parameters. The fuzzy solution is a fuzzy theorem’s unique idea, and its merit is that a decision maker understands the possibility of the solution visually. Moreover, the method proposed in this paper is applied to a diet problem, and an illustrative numerical example is also demonstrated. [In Japanese.]