Mehar approach for solving dual-hesitant fuzzy transportation problem with restrictions

Abstract

Recently, a new type of transportation problems (named as dual-hesitant fuzzy transportation problem) as well as an approach to find the optimal solution of dual-hesitant fuzzy transportation problems have been proposed in the literature. In this paper, some dual-hesitant fuzzy transportation problems are considered to show that the existing approach is inappropriate as (i) The existing approach fails to find the optimal solution of dual-hesitant fuzzy transportation problems. (ii) On applying the existing approach different optimal transportation costs are obtained corresponding to alternative optimal solutions. Also, to resolve the inappropriateness of the existing approach, a new expression (named as Mehar score function) is proposed to transform a dual-hesitant fuzzy set into a real number. Furthermore, a new approach (named as Mehar approach), based upon the proposed Mehar score function, is proposed to find the optimal solution of dual-hesitant fuzzy transportation problems.

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Acknowledgements

The authors would like to thank the corresponding Editor Dr.Manoj Kumar Tiwari and the anonymous reviewers for the constructive suggestions which have led to an improvement in both the quality and clarity of the paper. Dr. Parmpreet Kaur would like to thank the University Grants Commission (UGC) for the financial support under the minor research Project (KCP/2019/1439-44) entitled “Ranking of fuzzy numbers and its applications” under UGC CPE scheme for faculty enrichment.

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Correspondence to Amit Kumar.

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Kumar, A., Appadoo, S.S. & Kaur, P. Mehar approach for solving dual-hesitant fuzzy transportation problem with restrictions. Sādhanā 45, 77 (2020). https://doi.org/10.1007/s12046-020-01325-1

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Keywords

  • Dual-hesitant fuzzy set
  • transportation problems
  • score function