Satisficing solutions and duality in interval and fuzzy linear programming

  • Authors:

  • Masahiro Inuiguchi;Jaroslav Ramik;Tetsuzo Tanino;Milan Vlach

  • Affiliations:

  • Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, 565-0871 Osaka, Japan;Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Brafova 7, 701 03 Ostrava 1, Czech Republic;Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, 565-0871 Osaka, Japan;Graduate School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292 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 introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions--the necessary tools for dealing with such problems. In this way, we show that the class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems we define the concept of duality and prove the weak and strong duality theorems. Further, we define a class of interval linear programming problems as a special subclass of FLP problems and apply the previous results to this special case.