Multiobjective Two-Level Simple Recourse Programming Problems with Discrete-Type Fuzzy Random Variables and Optimistic and Pessimistic Pareto Stackelberg Solutions

In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes his/her multiple objective functions independently, shortages and excesses arising from the violation of the constraints with discrete-type LR fuzzy random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, we introduce new solution concepts called an optimistic and pessimistic Pareto Stackelberg solutions for the leader. It is shown that such optimistic and pessimistic Pareto Stackelberg solutions can be obtained by solving weighting problems of the leader. We propose an interactive algorithm to obtain a satisfactory solution of the leader from among an optimistic or pessimistic Pareto Stackelberg solution set.