Interactive Fuzzy Programming for a Decentralized Two-level Linear Programming Problem - Nishizaki, Ichiro; KUBOTA, Keiichi; UEMURA, Yoshio; SAKAWA, Masatoshi (Journal of Japan Society for Fuzzy Theory and Systems, 1999)
This paper persents interactive fuzzy programming for a decentralized two-level linear programming problem with one decision maker (DM) at the upper level and multiple DMs at the lower level. The interactive method consists of two phase. In the first phase, after determining the fuzzy goals of the DM 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. 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 permissible 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. Moreover, the derived satisfactory solution is an M-Pareto optimal solution in the satisfactory space.