Interactive Decision Making for Multiobjective Fuzzy Random Programming Problems with Simple Recourse through a Fractile Model

In this paper, we focus on multiobjective fuzzy random programming problems with simple recourse through a fractile optimization model, in which fuzzy random variables coefficients are involved in equality constraints, and random variables coefficients are involved in the objective functions. In the proposed method, equality constraints with fuzzy random variables are defined on the basis of a possibility measure and a two-stage programming method. To deal with the objective functions involving random variable coefficients, a fractile optimization model is applied. For a given permissible possibility level and/or permissible probability levels specified by the decision maker, several kinds of Pareto optimality concepts are introduced. Interactive decision making methods are proposed to obtain a satisfactory solution from among a Pareto optimal solution set. The proposed method is applied to a farm planning problem in the Philippines, in which it is assumed that the amount of water resource in dry season is represented as a fuzzy random variable.