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An approach based on combining Choquet integral and TOPSIS methods to uncertain MAGDM problems

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Abstract

In this paper, we considered the defined intuitionistic fuzzy numbers (IFNs) on real numbers and proposed a new method based on Hamacher operators to operate with membership and non-membership degrees of the given IFN in aggregation process. Also, a new method will be introduced to compute the distance between IFNs. These methods will be applied to solve multi-attribute group decision-making (MAGDM) problems, in which IFNs were used to model the arising uncertainty from human judgments or assessments. To do it, Choquet integral, as a powerful tool in both independent and interactive criteria, will be used individually or as a tool to provide appropriate conditions for application of TOPSIS method. The applicability of these methods is illustrated by numerical examples.

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Acknowledgements

This research was supported by Velayat University, Iranshahr, Iran (No. ...). We thank our colleagues from Velayat University who provided insight and expertise that greatly assisted the research, although they may not agree with all of the interpretations/conclusions of this paper. We would also like to show our gratitude to the Editors for sharing their pearls of wisdom with us, to anonymous Reviewers for their comments on the manuscript, although any errors are our own and should not tarnish the reputations of these esteemed persons.

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Authors and Affiliations

  1. Department of Mathematics, Velayat University, Iranshahr, Iran

    Abazar Keikha

  2. School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, Punjab, 147004, India

    Harish Garg

  3. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Hassan Mishmast Nehi

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  1. Abazar Keikha
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  2. Harish Garg
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  3. Hassan Mishmast Nehi
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Correspondence to Abazar Keikha.

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Keikha, A., Garg, H. & Mishmast Nehi, H. An approach based on combining Choquet integral and TOPSIS methods to uncertain MAGDM problems. Soft Comput 25, 7181–7195 (2021). https://doi.org/10.1007/s00500-021-05682-9

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