Interactive Decision Making Based on Level Sets and Fractile Criterion Optimization Model for Two-level Linear Programming Problems Involving Fuzzy Random Variable Coefficients

Abstract

In this paper, we focus on fuzzy random two-level linear programming problems. First, we reformulate the given problem as an alpha-two-level stochastic linear programming problem where the degree of realization of the problem is guaranteed to be greater than or equal to alpha. Introducing fuzzy goals to quantify the ambiguity in the judgement of decision makers (DMs), we transform the reformulated problem into a problem to maximize the satisfactory degree of each fuzzy goal. Next, since the satisfactory degree of each fuzzy goal in the transformed problem is a random variable, it is reduced to a deterministic two-level programming problem based on fractile criterion optimization. Then, for the reduced problem, under the assumption of the cooperative relationship between DMs, we propose an interactive decision making method to derive a satisfactory solution through interactions such that the DM updates the degree of realization of the problem and the minimal satisfactory degree.