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On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions

Author

Listed:
  • Sumati Mahajan

    (Indian Institute of Technology Roorkee)

  • S. K. Gupta

    (Indian Institute of Technology Roorkee)

Abstract

Intuitionistic fuzzy set theory is a generalized version of classical fuzzy set theory, where membership degree of acceptance and membership degree of rejection are both measured. In the present study, we formulate a balanced transportation problem with multiple objectives having all parameters and variables as intuitionistic fuzzy numbers. The problem is first reduced to a crisp multiobjective transportation problem using accuracy function on each objective function and then an algorithm is proposed to solve the problem. In the solution procedure, linear, exponential and hyperbolic membership functions are used to tackle intuitionistic fuzzy constraints related with each objective. To show the relations among the intuitionistic fuzzy transportation problem, its equivalent crisp formulation and the problems obtained by applying different membership functions, various theorems are established. Finally, two numerical examples are illustrated to clarify the steps involved in the proposed algorithm and to draw the comparison among linear, exponential and hyperbolic membership functions.

Suggested Citation

  • Sumati Mahajan & S. K. Gupta, 2021. "On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions," Annals of Operations Research, Springer, vol. 296(1), pages 211-241, January.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-019-03318-8
    DOI: 10.1007/s10479-019-03318-8
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    References listed on IDEAS

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