Bipolar \(M\)-parametrized \(N\)-soft sets‎: ‎a gateway to informed decision-making

Volume 36, Issue 1, pp 121--141 https://dx.doi.org/10.22436/jmcs.036.01.08

Publication Date: July 02, 2024 Submission Date: March 06, 2024 Revision Date: May 08, 2024 Accteptance Date: May 16, 2024

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Authors

S. Y‎. ‎ Musa - Department of Mathematics‎, ‎College of Education‎, University of Zakho‎, Zakho 42002, Zakho‎, Iraq. B. A‎. ‎ Asaad - Department of Computer Science‎, ‎College of Science, ‎Cihan University-Duhok, ‎Duhok 42001, Duhok, Iraq. - Department of Mathematics‎, ‎College of Science, University of Zakho‎, ‎Zakho 42002, ‎Zakho, Iraq.

Abstract

\(M\)-parametrized \(N\)-soft set (MPNSS)‎, ‎an extension of \(N\)-soft set (\(N\)-SS) theory‎, ‎is instrumental in addressing the challenges of assigning non-binary evaluations to both alternatives and attributes‎. ‎Recognizing the inherent duality in human decision-making‎, ‎where choices are influenced by both positive and negative aspects‎, ‎we enhance the MPNSS framework by incorporating bipolarity‎. ‎This addition‎, ‎aimed at capturing the dual nature of decision processes‎, ‎results in the development of bipolar \(M\)-parametrized \(N\)-soft set (BMPNSS) model‎. ‎In the context of BMPNSS‎, ‎we present some related definitions such as incomplete‎, ‎negatively efficient‎, ‎positively efficient‎, ‎and totally efficient‎. ‎Additionally‎, ‎for the complement of MPNSS‎, ‎we introduce four distinct definitions‎: ‎complement‎, ‎weak complement‎, ‎top weak complement‎, ‎and bottom weak complement‎. ‎Set-theoretic operations‎, ‎including extended and restricted union and intersection‎, ‎are explored accompanied by a discussion of their properties‎, ‎providing a comprehensive understanding of the behavior of these operations within the BMPNSS framework‎. ‎To facilitate understanding‎, ‎we include an illustrative example‎. ‎The decision-making procedure introduces alternative ranking based on extended choice and extended weight choice values‎, ‎demonstrated through a numerical example‎. ‎In our comparative analysis‎, ‎BMPNSS is positioned against existing models‎, ‎emphasizing its distinctive features and advantages in diverse decision-making scenarios‎.

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Keywords

• Bipolar \(M\)-parametrized \(N\)-soft set
• \(M\)-parametrized \(N\)-soft set
• \(N\)-soft set \sep decision-making
• algorithm

MSC

•  03E72
•  03E99
•  68T37
•  68T30

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