# Interactive Decision Making for Multiobjective Simple Recourse Programming Problems with Discrete or Continuous Fuzzy Random Variables

## Abstract

In this paper, we formulate multiobjective simple recourse programming problems in which discrete fuzzy random variables or continuous ones are involved in equality constraints. In the proposed methods, equality constraints with two types of fuzzy random variables are defined on the basis of a possibility measure and and a two-stage programming method. For a given permissible possibility level specified by the decision maker, a Pareto optimality concept is introduced. Both an interactive linear programming algorithm for discrete fuzzy random variables and an interactive convex programming algorithm for continuous fuzzy random variables are developed to obtain a satisfactory solution from among a Pareto optimal solution set. The proposed methods are applied to farm planning problems in the Philippines, in which it is assumed that the amount of water supply in dry season is represented as a discrete fuzzy random variable or a continuous one.

## Keywords

Programming Problem Equality Constraint Pareto Optimal Solution Reference Objective Satisfactory Solution## References

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