Linear programming with graded ill-known sets

Authors:
Shizuya Kawamura;Masahiro Inuiguchi
Affiliations:
Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan;Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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Abstract

In this paper, we investigate linear programming problems with graded ill-known sets (GIS-LP problems). Because a graded ill-known set (GIS) is defined by a possibility distribution on the power set, treatments of GISs are usually complex. To treat them in a simpler way at the expense of precision, the representation by upper and lower approximations have been investigated. Once these approximations are applied, the original GIS is not usually restored. We propose a class of GISs restorable from the approximations. Utilizing the previous results in GISs, we formulate a GIS-LP problem based on the idea of symmetric model in possibilistic programming. We show that the formulated GIS-LP problem is solved by a bisection method together with the simplex method. A simple numerical example is given.