Interactive fuzzy programming for decentralized two-level linear programming problems

This paper presents interactive fuzzy programming for a decentralized two-level linear programming problem with a single decision maker (DM) at the upper level and multiple DMs at the lower level. The interactive method consists of two phases. In the first phase, after determining the fuzzy goals of the DMs at both levels, the DM at the upper level subjectively specifies a minimal satisfactory level. Taking into consideration overall satisfactory balance between the two levels, the DM at the upper level updates the minimal satisfactory level if necessary, and a tentative solution is obtained. In the second phase, consulting the ratios of satisfaction between the DM at the upper level and each of the DMs at the lower level, the DM at the upper level specifies maximal satisfactory levels to the DMs at the lower level and updates them if necessary. A satisfactory solution can be derived efficiently through the interactive procedure of the two phases. A numerical example illustrates the proposed method. (C) 2002 Elsevier Science B.V. All rights reserved.