Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters

This paper presents interactive fuzzy programming for multi-level linear pr ogramming problems with fuzzy parameters. In fuzzy programming for multi-le vel linear programming problems, recently developed by Lai et al., since th e fuzzy goals are determined for both an objective function and decision va riables at the upper level, undesirable solutions are produced when these f uzzy goals are inconsistent. In order to overcome such problems, after elim inating the fuzzy goals for decision variables, interactive fuzzy programmi ng for multi-level linear programming problems with fuzzy parameters is pre sented. In our interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficien tly by updating the satisfactory degrees of decision makers with considerat ions of overall satisfactory balance among all levels. Illustrative numeric al examples for two-level and three-level linear programming problems are p rovided to demonstrate the feasibility of the proposed method. (C) 2000 Els evier Science B.V. All rights reserved.