Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters

In this paper, we present interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Using the level sets of fuzzy parameters, the corresponding nonfuzzy two-level linear fractional programming problem is introduced. In our interactive method, after determining fuzzy goals of decision makers at both levels, a satisfactory solution is derived efficiently by updating a minimal satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. The satisfactory solution well-balanced between both levels is easily computed by combined use of the bisection method, the phase one of the simplex method and the variable transformation method by Charnes and Cooper. An illustrative numerical example for two-level linear fractional programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method. (C) 2000 Elsevier Science B.V. All rights reserved.