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Grey relational analysis method for SVTrNN based multi-attribute decision making with partially known or completely unknown weight information

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Abstract

Single-valued trapezoidal neutrosophic number (SVTrNN), an extension of single-valued neutrosophic set, effectively deals with indeterminate and incomplete information in multi-attribute decision making (MADM) problem. In this paper, we extend the grey relational analysis (GRA) method for solving SVTrNN based MADM problem, where the weight information of attributes is partially known or completely unknown. Following the classical GRA method, we define grey relational co-efficient using a new distance measure. We develop two optimization models to determine the weights of the attributes. We calculate grey positive and negative relational degrees and define the relative closeness co-efficient of each alternative to determine the best alternative. We take a numerical example to validate the proposed approach and compare the proposed method with other exiting methods. It is observed from the numerical study that the proposed GRA method has an advantage over the existing methods for solving SVTrNN based MADM problem with partially known or completely unknown attribute weight information.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions on an earlier version of this paper. This research was supported by the Council of Scientific and Industrial Research (CSIR), Govt. of India, File No. 09/096(0945)/2018-EMR-I

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    Bibhas C. Giri, Mahatab Uddin Molla & Pranab Biswas

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  1. Bibhas C. Giri
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  2. Mahatab Uddin Molla
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  3. Pranab Biswas
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Correspondence to Bibhas C. Giri.

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Giri, B.C., Molla, M.U. & Biswas, P. Grey relational analysis method for SVTrNN based multi-attribute decision making with partially known or completely unknown weight information. Granul. Comput. 5, 561–570 (2020). https://doi.org/10.1007/s41066-019-00174-6

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