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Fuzzy linear optimization

In: Linear Optimization Problems with Inexact Data

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  • J. Ramík

Abstract

5.12 Conclusion In this chapter we have proposed a new general approach to fuzzy single and multicriteria linear programming problems with fuzzy coefficients. A unifying concept of this approach is the concept of a fuzzy relation, particularly fuzzy extension of the inequality or equality relation and the concept of an aggregation operator. We have formulated the FLP problem, defined a feasible solution of the FLP problem and dealt with the problem of “optimal solution” of FLP problems. Two approaches have been introduced: the satisficing solution based on externalgoals modeled by fuzzy quantities, and the α-efficient (nondominated) solution. Then our interest has been focused on the problem of duality in FLP. Finally, we have also dealt with the multicriteria case. We have formulated a fuzzy multicriteria linear programming problem, defined a compromise solution and derived basic results. The chapter has been closed with a numerical example.

Suggested Citation

  • J. Ramík, 2006. "Fuzzy linear optimization," Springer Books, in: Linear Optimization Problems with Inexact Data, chapter 5, pages 117-164, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-32698-6_5
    DOI: 10.1007/0-387-32698-7_5
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