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A Fuzzy Programming Approach to Structured Linear Programs

  • M. Sakawa
  • M. Inuiguchi
  • K. Kato
  • K. Sawada
Part of the Theory and Decision Library book series (TDLD, volume 16)

Abstract

In this paper, we focus on large-scale linear programming problems with block angular structure by assuming that the decision maker (DM) may have a fuzzy goal for the objective function and fuzzy constrains for the coupling constraints. Having elicited the corresponding linear membership functions through the interaction with the DM, we adopt the convex fuzzy decision. Then if some simple conditions are satisfied, it is shown that the formulated problem can be reduced to a number of independent linear subproblems and the satisfying solution for the DM is directly obtained just only solving the subproblems.

Keywords

Decision Maker Fuzzy Goal Coupling Constraint Fuzzy Constraint Linear Membership Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Dantzig, G. B. and Wolfe, P. (1961) The decomposition algorithm for linear programming, Econometrica 29, 767–778.CrossRefzbMATHMathSciNetGoogle Scholar
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    Lasdon, L. S. (1970) Optimization Theory for Large Systems, Macmillan, New York.zbMATHGoogle Scholar
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    Sakawa, M. (1993) Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press, New York.zbMATHGoogle Scholar
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    Zimmermann, H.-J. (1991) Fuzzy Set Theory and Its Applications, 2nd Revised Edition, Kluwer Academic Publishers, Boston.zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • M. Sakawa
    • 1
  • M. Inuiguchi
    • 1
  • K. Kato
    • 1
  • K. Sawada
    • 2
  1. 1.Department of Industrial and Systems Engineering, Faculty of EngineeringHiroshima UniversityHigashi-Hiroshima 724Japan
  2. 2.Information System CenterMatsushita Electric Works, LtdKadoma, Osaka 571Japan

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