An interactive fuzzy satisfying method for multiobjective block angular linear fractional programming problems with parameters.

In this paper we have introduced a nonfuzzy α-multiobjective linear fractional programming problem, for an α set up to satisfy the DM as much as possible and such that the elements of the coefficient vectors are equal to or greater than α. These vectors are formed with membership degrees of the fuzzy number membership functions involved in the block angular linear fractional programming problem with fuzzy parameters. Simultaneously, we provide for the fuzzy goals of the DM with respect to each objective function by the use of membership functions also containing nonlinear functions. Furthermore, we propose an interactive decision-making method that determines an approximate M-α-Pareto optimal solution in the minimax sense for reference membership values set up by the DM subjectively; if the DM is not satisfied with it, this method elicits a DM satisfying solution from the M-α-Pareto optimal solutions by interactive upgrading of the membership values and/or the α value. With respect to the minimax problem used to determine the M-α-Pareto optimal solution, this one could be determined by application of the Dantzig-Wolfe decomposition principle and the Ritter partitioning procedure, since the techniques introduced here produce block angular problems with only coupling constraints and block angular problems with coupling constraints and coupling variables. The applications of the proposed interactive decision-making technique to actual decision-making conditions are left for future investigation. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(12): 45–54, 1998 [ABSTRACT FROM AUTHOR]