An interactive fuzzy satisficing method based on the fractile optimization model using possibility and necessity measures for a fuzzy random multiobjective linear programming problem

Abstract

This paper treats a multiobjective linear programming problem in which the coefficients contained in the objective function of the problem are fuzzy random variables. First, in order to take into account ambiguities of judgment by a human decision maker, fuzzy objectives are introduced. Subsequently, we consider a problem of maximizing the possibility and necessity of the objective function value to satisfy the fuzzy objectives. Since these degrees vary stochastically, a formulation is based on the fractile optimization model in a stochastic programming method. A process is presented for equivalent transformation to a deterministic multiobjective nonlinear fractional programming method. For the transformed multiobjective programming problem, an interactive fuzzy satisficing method that derives a satisfactory solution of the decision maker through interactions with the decision maker is proposed. It is shown that the global optimum solution of problems solved iteratively by an interactive process can be derived by means of an extended Dinkelbach-type algorithm. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(5): 20–28, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20136