m-Polar N-soft set and its application in multi-criteria decision-making: m-Polar N-soft set and its application

This study introduces an innovative model termed the m -polar N -soft set, designed to meet the urgent need for evaluating decision-making criteria using integers in a multi-polar fashion. Unlike existing models such as soft sets and N -soft sets, which use binary and integer values respectively in a single polar manner, the proposed model enables decision-makers to utilize integers multi-polarly. The paper explores various operations on m -polar N -soft sets, including union, intersection, addition, subtraction, complements, and Product/Sum operations. These operations are elucidated through real-life examples to highlight their properties. Additionally, the study presents two multi-criteria decision-making algorithms, catering to both weighted and non-weighted scenarios, with a practical application included. A comparative analysis between the proposed and existing approaches demonstrates the efficacy and stability of the proposed model, supported by graphical visualization. In conclusion, the m -polar N -soft set model not only generalizes existing models but also offers enhanced accuracy for solving real-life multi-criteria decision-making problems.