On m-polar Diophantine Fuzzy N-soft Set with Applications

Introduction: In this paper, we present a novel hybrid model m-polar Diophantine fuzzy N-soft set and define its operations. Methods: We generalize the concepts of fuzzy sets, soft sets, N-soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets and Pythagorean fuzzy N-soft sets by incorporating our proposed model. Additionally, we define three different sorts of complements for Pythagorean fuzzy N-soft sets and examine few outcomes, which do not hold in Pythagorean fuzzy N-soft sets complements unlike to crisp set. We further discuss (alpha, beta, gamma) -cut of m-polar Diophantine fuzzy N-soft sets and their properties. Lastly, we prove our claim that the defined model is a generalization of the soft set, N-soft set, fuzzy N-soft set, intuitionistic fuzzy N soft set, and Pythagorean fuzzy N-soft set. Results: m-polar Diophantine fuzzy N-soft set is more efficient and an adaptable model to manage uncertainties as it also overcomes drawbacks of existing models, which are to be generalized. Conclusion: We introduced the novel concept of m-polar Diophantine fuzzy N-soft sets (MPDFNS sets).

Automated summary

This paper presents a novel hybrid model called m-polar Diophantine fuzzy N-soft set and defines its operations. The model proves to be more efficient and adaptable in managing uncertainties, overcoming the drawbacks of existing models. It generalizes several concepts and introduces the concept of m-polar Diophantine fuzzy N-soft sets.