Interactive fuzzy programming for two-level linear fractional programming problems - Sakawa, Masatoshi; Nishizaki, Ichiro (Fuzzy sets and systems, 2001)
This paper presents interactive fuzzy programming for two-level linear fractional programming problems with the essentially cooperative decision makers. In our interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is efficiently derived by updating the satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. In an interactive process, optimal solutions to the formulated programming problems are obtained by combined use of the bisection method and the phase one of linear programming and the variable transformation by Charnes and Cooper. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.