Computing a Pareto-optimal solution for multi-objective flexible linear programming in a bipolar framework

Abstract

In this paper, we study the multi-objective flexible linear programming (MOFLP) problems (or fuzzy multi-objective linear programming problems) in the heterogeneous bipolar framework. Bipolarity allows us to distinguish between the negative and the positive preferences. Negative preferences denote what is unacceptable while positive preferences are less restrictive and express what is desirable. This viewpoint enables us to handle fuzzy sets representing constraints and objective functions separately and combine them in distinct ways. In this paper, a solution concept of Pareto-optimality for MOFLP problems is defined and an approach is proposed to single out such a solution for MOFLP with highest possible degree of feasibility.

Keywords:

• flexible linear programming
• fuzzy sets
• feasibility degree
• Pareto-optimal solution
• bipolarity

Acknowledgements

The first author thanks the National Board of Higher Mathematics (NBHM), India, for financial support for this research.