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 (α, β, γ) -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 Nsoft 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).