INTERACTIVE FUZZY-PROGRAMMING FOR MULTILEVEL LINEAR-PROGRAMMING PROBLEMS

This paper presents interactive fuzzy programming for multilevel linea r programming problems. In fuzzy programming for multilevel linear pro gramming problems, recently developed by Lai ct al., since the fuzzy g oals are determined for both an objective function and decision variab les at the upper level, undesirable solutions are produced when these fuzzy goals are inconsistent. In order to overcame such problems, afte r eliminating the fuzzy goals for decision variables, interactive fuzz y programming for multilevel linear programming problems is presented. In our interactive method, after determining the fuzzy goals of the d ecision makers at all levels, a satisfactory solution is derived effic iently by updating the satisfactory degrees of decision makers at the upper level with considerations of overall satisfactory balance among all levels. Illustrative numerical examples for two-level and for thre e-level linear programming problems are provided to demonstrate the fe asibility of the proposed method. (C) 1998 Elsevier Science Ltd. All r ights reserved.