Possibilistic Linear Programming Using General Necessity Measures Preserves the Linearity

Abstract

In this paper, a robust optimization approach to possibilistic linear programming problems is studied. After necessity measures and generation processes of logical connectives are reviewed, the necessity fractile optimization model of possibilistic linear programming problem is introduced as a robust optimization model. This problem is reduced to a linear semi-infinite programming problem. Assuming the convexity of the right parts of membership functions of fuzzy coefficients and the concavity of membership functions of fuzzy constraints, we investigate conditions on logical connectives for the problems to be reduced to linear programming problems. Several examples are given to demonstrate that necessity fractile optimization models are often reduced to linear programming problems.Keywordspossibilistic linear programmingnecessity measureimplication functionconjunction function