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On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions

  • S.I.: MOPGP 2017
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A Correction to this article was published on 30 August 2019

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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.

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Change history

  • 30 August 2019

    This erratum is published because vendor overlooked corrections related to Theorems 3 to 5.

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Acknowledgements

The authors sincerely acknowledge the valuable suggestions and recommendations of the anonymous reviewers, which has considerably improved the presentation and quality of the paper. The first author is also thankful to the Quality Improvement Programme cell of IIT Roorkee and Punjab Engineering College, Chandigarh along with All India Council of Technical Education for their support to carry out this work.

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Sumati Mahajan & S. K. Gupta

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  1. Sumati Mahajan
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  2. S. K. Gupta
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Correspondence to Sumati Mahajan.

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Mahajan, S., Gupta, S.K. On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions. Ann Oper Res 296, 211–241 (2021). https://doi.org/10.1007/s10479-019-03318-8

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