A novel decision-making technique based on T-rough bipolar fuzzy sets

Volume 33, Issue 3, pp 275--289 https://dx.doi.org/10.22436/jmcs.033.03.06

Publication Date: January 14, 2024 Submission Date: November 27, 2023 Revision Date: December 11, 2023 Accteptance Date: December 13, 2023

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Authors

N. Malik - Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan. M. Shabir - Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan. T. M. Al-shami - Department of Mathematics, Sana'a University, P.O. Box 1247, Sana'a, Yemen. - Department of Engineering Mathematics \(\&\) Physics, Faculty of Engineering \(\&\) Technology, Future University, New Cairo, Egypt. R. Gul - Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan. M. Arar - Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz, Riyadh, Saudi Arabia.

Abstract

In this paper, we hybridize the bipolar fuzzy set (BFS) theory with T-rough sets (T-RSs) and initiate the novel idea of T-rough BFSs (T-RBFSs). The concept presented in this article has never been discussed earlier. Moreover, we investigate the axiomatic systems of T-RBFSs in detail. Meanwhile, we address a decision-making (DM) problem having data endowed with fuzziness and bipolarity in the framework of the T-RBFSs. We also propose an algorithm for this application. This algorithm facilitates tackling the case when there is a team of decision-makers instead of a single decision-maker and when the objects of one set need to be approximated by grading the objects of some other set. Moreover, a practical application of T-RBFSs in DM problems is given, accompanied by a practical example, which provides the optimal and the worst decision between some objects. Finally, a comparative analysis of the recommended study with several prevailing approaches is given to endorse the advantages of the suggested research.

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Keywords

• T-rough sets
• bipolar fuzzy sets
• T-rough bipolar fuzzy sets
• decision-Making

MSC

•  03E72
•  62C86

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