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.
\(M\)-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.
S. Y. Musa, B. A. Asaad, Bipolar \(M\)-parametrized \(N\)-soft sets: a gateway to informed decision-making, Journal of Mathematics and Computer Science, 36 (2025), no. 1, 121--141
Musa S. Y. , Asaad B. A. , Bipolar \(M\)-parametrized \(N\)-soft sets: a gateway to informed decision-making. J Math Comput SCI-JM. (2025); 36(1):121--141
Musa, S. Y. , Asaad, B. A. . "Bipolar \(M\)-parametrized \(N\)-soft sets: a gateway to informed decision-making." Journal of Mathematics and Computer Science, 36, no. 1 (2025): 121--141
