Application of Graded Ill-known Sets to Linear Programming Problems

Abstract

In this paper, we investigate linear programing problems with graded ill-known sets (GIS-LPPs). Because a graded ill-known set (GIS) is defined by a possibility distribution on the power set, treatments of GISs are usually complex. Therefore, the representation using upper and lower approximations have been proposed. However, such representation cannot always recover the original GIS. We propose a class of GISs which are recoverable. Utilizing the previous results in GISs, we formulate a GIS-LPP by using symmetric model. We show that the formulated GIS-LPP is solved by a bisection method together with the simplex method.