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Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions

Author

Listed:
  • Amit Kumar

    (Thapar University)

  • Anila Gupta

    (Thapar University)

Abstract

Mukherjee and Basu proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-mentioned method. Two new methods are proposed for solving such type of fuzzy assignment problems and fuzzy travelling salesman problems. The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed methods, a fuzzy assignment problem and a fuzzy travelling salesman problem is solved. The proposed methods are easy to understand and apply to find optimal solution of fuzzy assignment problems and fuzzy travelling salesman problems occurring in real life situations.

Suggested Citation

  • Amit Kumar & Anila Gupta, 2011. "Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions," Fuzzy Information and Engineering, Springer, vol. 3(1), pages 3-21, March.
    • Handle: RePEc:spr:fuzinf:v:3:y:2011:i:1:d:10.1007_s12543-011-0062-0
    DOI: 10.1007/s12543-011-0062-0
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    References listed on IDEAS

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    1. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2001. "Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: A case study," European Journal of Operational Research, Elsevier, vol. 135(1), pages 142-157, November.
    2. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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