Oblique fuzzy vectors and their use in possibilistic linear programming

Authors:
Masahiro Inuiguchi;Jaroslav Ramik;Tetsuzo Tanino;Milan Vlach
Affiliations:
Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan;Department of Mathematical Methods in Economics, School of Business Administration, Silesian University, University Square 76, 733 40 Karviná, Czech Republic;Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan;Graduate School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Tatsunokuchi, Japan
Venue:
Fuzzy Sets and Systems - Special issue: Interfaces between fuzzy set theory and interval analysis
Year:
2003

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Abstract

In this paper, we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers. Oblique fuzzy vectors are extensions of fuzzy numbers and vectors of non-interactive fuzzy numbers. The interactivity among fuzzy numbers can be treated by a non-singular matrix in an oblique fuzzy vector. We discuss characterization of an oblique fuzzy vector and the tractability of manipulation of oblique fuzzy vectors in fuzzy linear functions. Moreover, we discuss possibilistic linear programming problems with oblique fuzzy vectors. It is shown that the possibilistic linear programming problems are reduced to linear programming problems with a special structure.