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International Fuzzy Systems Association World Congress

IFSA 2003: Fuzzy Sets and Systems — IFSA 2003 pp 718–724Cite as

A Global Optimization Method for Solving Fuzzy Relation Equations

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2715))

Abstract

A system of fuzzy relation equations can be reformulated as a global optimization problem. The optimum solution of this new model corresponds to a solution of the system of fuzzy relation equations whenever the solution set of the system is nonempty. Moreover, even if the solution set of the fuzzy relation equations is empty, a solution to the global optimization problem provides a point such that the difference between the right and the left hand side of the fuzzy relation equations is minimized. The new global optimization problem has a nonconvex and nondifferentiable objective function. Therefore, a recent stochastic search approach is applied to solve this new model. The performance of the approach is tested on a set of problems with different dimensions.

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Author information

Authors and Affiliations

  1. Erasmus Research Institute of Management, Erasmus University, Postbus 1738, 3000 DR, Rotterdam, The Netherlands

    Ş İlker Birbil

  2. Department of Industrial Engineering, Galatasaray University, Çırağan Caddesi No: 36, 34357, Ortaköy/İstanbul, Turkey

    Orhan Feyzioğlu

Authors
  1. Ş İlker Birbil
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  2. Orhan Feyzioğlu
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Taner Bilgiç

  2. Dept. of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, 9000, Gent, Belgium

    Bernard De Baets

  3. Department of Electrical and Electronics Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Okyay Kaynak

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© 2003 Springer-Verlag Berlin Heidelberg

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Cite this paper

Birbil, Ş.İ., Feyzioğlu, O. (2003). A Global Optimization Method for Solving Fuzzy Relation Equations. In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_86

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  • DOI: https://doi.org/10.1007/3-540-44967-1_86

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40383-8

  • Online ISBN: 978-3-540-44967-6

  • eBook Packages: Springer Book Archive

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