An extension of grey relational analysis for interval-valued fuzzy soft sets

Muhammad Touqeer; M Nauman Saeed; Nadeem Salamat; Muhammad Mustahsan

doi:10.17485/IJST/v13i31.115

Article

An extension of grey relational analysis for interval-valued fuzzy soft sets

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v13i31.115

Year: 2020, Volume: 13, Issue: 31, Pages: 3176-3187

Review Article

An extension of grey relational analysis for interval-valued fuzzy soft sets

Muhammad Touqeer^1*, M Nauman Saeed¹, Nadeem Salamat²,Muhammad Mustahsan³

¹Basic Sciences Department, University of Engineering and Technology, Taxila, Pakistan
²Khwaja Fareed University of Engineering and Information Technology, RYK, Pakistan
³Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

*Corresponding Author
Email: [email protected]

Received Date:02 April 2020, Accepted Date:04 July 2020, Published Date:27 August 2020

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Background: Neither any analytical (nor numerical) nor any statistical approach is often helpful in a situation where every person has his/her own choice. To cope with such situations usually we have to use fuzzy sets in combination with soft sets, which consist of predicates and approximate value sets as their images. Material: Choice values and comparison table techniques are two common decision-making techniques, which often don’t result in same preference order or optimal choice. To overcome this kind of situation in decision-making problems, grey relational analysis method is used to get on a final decision. Method: Here we have used grey relational analysis method involving “interval-valued fuzzy soft sets” and “AND operation” to deal with such kind of problems. Our approach is also a correction to the method used by Kong et al.(1), where the Uni-Int technique is incorrectly used in case of soft sets instead of fuzzy soft sets. Result: The proposed method is effective in seeking an optimal choice in the case when common decision-making techniques fail to get on a final decision. Conclusion: By using grey relational analysis, a suitable method to choose one object from different choices has been proposed. It overcomes the grayness in decision-making problems for getting on a final decision when one gets too many options and finds it difficult to choose an optimal choice.

Keywords: Fuzzy soft set; Grey relational analysis; Un-Int; interval-valued fuzzy soft set

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© 2020 Touqeer et al.This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee).