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

In this paper, we present interactive fuzzy programming for two-level linea r fractional programming problems with fuzzy parameters. Using the level se ts of fuzzy parameters, the corresponding nonfuzzy two-level linear fractio nal programming problem is introduced. In our interactive method, after det ermining fuzzy goals of decision makers at both levels, a satisfactory solu tion is derived efficiently by updating a minimal satisfactory level of the decision maker at the upper level with considerations of overall satisfact ory balance between both levels. The satisfactory solution well-balanced be tween both levels is easily computed by combined use of the bisection metho d, the phase one of the simplex method and the variable transformation meth od by Charnes and Cooper. An illustrative numerical example for two-level l inear fractional programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method. (C) 2000 Elsevier Scien ce B.V. All rights reserved.