Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments.

► We tackle a new multiobjective programming problem with random fuzzy variables.
► We propose a new model optimizing possibilistic value at risk, called pVaR.
► We prove that the original problem can be transformed into a deterministic problem.
► We provide an interactive algorithm to obtain a satisficing solution.
► Our algorithm can exactly obtain Pareto optimal solutions using a convex property.