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Fuzzy Combinatorial Optimization Problems

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Handbook of Combinatorial Optimization

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Abstract

Decision-making is an ongoing process for humankind. Many of these real-world decisions can be modeled using the problems contained in the generalized area of combinatorial optimization. Another area with recent advancements is fuzzy logic.

This chapter is concerned about the fuzzy solution approaches of combinatorial optimization problems. First section presents the fuzzy graph theory. Fuzzy linear programming and fuzzy integer programming are explained in second and third sections. Fuzzy spanning trees, fuzzy shortest path, fuzzy network flows, and the fuzzy minimum cost flow problems are introduced at Sects. 4–7. Fuzzy matching algorithm, fuzzy matroids, and fuzzy approximation algorithm are discussed in Sects. 8–10. Basic information on fuzzy knapsack and fuzzy bin-packing problems is given in Sects. 11 and 12. Fuzzy multicommodity flows and edge-disjoint paths are explained in Sect. 13 in detail with four subsections. Fuzzy network design problems and fuzzy traveling salesman problem are provided in Sects. 14 and 15 respectively. Finally, fuzzy facility location is presented in the last section.

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Authors and Affiliations

  1. Faculty of Engineering, Department of Industrial and System Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Faculty of Engineering, Department of Industrial Engineering, Erciyes University, Kayseri, Turkey

    Emel Kızılkaya Aydogan

  3. Faculty of Engineering, Department of Industrial Engineering, Erciyes University, Kayseri, Turkey

    Feyza Gurbuz

  4. Department of Business Administration, Erciyes University, Kayseri, Turkey

    Ozgur Demirtas

  5. Faculty of Engineering, Department of Industrial Engineering, Gazi University, Ankara, Turkey

    Birce Boga Bakirli

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  1. Panos M. Pardalos
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  2. Emel Kızılkaya Aydogan
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  3. Feyza Gurbuz
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  4. Ozgur Demirtas
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  5. Birce Boga Bakirli
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Correspondence to Panos M. Pardalos , Emel Kızılkaya Aydogan , Ozgur Demirtas or Birce Boga Bakirli .

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Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Pardalos, P.M., Aydogan, E.K., Gurbuz, F., Demirtas, O., Bakirli, B.B. (2013). Fuzzy Combinatorial Optimization Problems. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_68

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