Interactive decision making with fuzzy goals for simple recourse in multiobjective stochastic programming problems

Abstract

In this paper, we focus on multiobjective stochastic programming problems, and propose two interactive fuzzy decision-making methods to obtain a satisfactory solution of a decision maker. In the proposed methods, equality constraints with random variables are formulated on the basis of the two-stage programming method, in which two kinds of random variables, i.e., continuous ones and discrete ones, are considered, respectively. Under the assumption that the decision maker has fuzzy goals not only for the original objective functions but also for the expectations of shortages and excesses for the violation of the equality constraints, the M-α-Pareto optimality concept is introduced, and two interactive fuzzy decision-making methods are proposed to obtain a satisfactory solution from among an M-α-Pareto optimal solution set. The proposed method is applied to a farm planning problem in the Philippines, in which it is assumed that an amount supplied of water resource in dry season is represented as a continuous or discrete random variable.