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A method to solve linear programming problem with interval type-2 fuzzy parameters

Author

Listed:
  • Pradip Kundu

    (Indian Institute of Science Education and Research Kolkata)

  • Saibal Majumder

    (National Institute of Technology, Durgapur)

  • Samarjit Kar

    (National Institute of Technology, Durgapur)

  • Manoranjan Maiti

    (Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University)

Abstract

In this paper, we propose a method to solve linear programming network problems with constraints using interval type-2 fuzzy variables. The method is developed using generalized credibility measure, and lower and upper membership functions of an interval type-2 fuzzy variable. This method has been applied to solve a solid transportation problem with availabilities and demands of a product, and conveyance capacities, which are represented by trapezoidal interval type-2 fuzzy variables. Moreover, we have also shown that different types of problems with objective function having interval type-2 fuzzy parameters can be solved using the proposed method. Apart from a solid transportation problem, we demonstrate its applicability by solving two different network problems: (i) a shortest path problem and (ii) a minimum spanning tree problem. Suitable numerical examples are provided to illustrate the proposed method

Suggested Citation

  • Pradip Kundu & Saibal Majumder & Samarjit Kar & Manoranjan Maiti, 2019. "A method to solve linear programming problem with interval type-2 fuzzy parameters," Fuzzy Optimization and Decision Making, Springer, vol. 18(1), pages 103-130, March.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:1:d:10.1007_s10700-018-9287-2
    DOI: 10.1007/s10700-018-9287-2
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    References listed on IDEAS

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    1. Jimenez, F. & Verdegay, J. L., 1999. "Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach," European Journal of Operational Research, Elsevier, vol. 117(3), pages 485-510, September.
    2. Pradip Kundu & Samarjit Kar & Manoranjan Maiti, 2014. "Multi-objective solid transportation problems with budget constraint in uncertain environment," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1668-1682, August.
    3. Chen, Ting-Yu & Chang, Chien-Hung & Rachel Lu, Jui-fen, 2013. "The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making," European Journal of Operational Research, Elsevier, vol. 226(3), pages 615-625.
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