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

Abstract

In this paper, we present a novel hybrid model m-polar Diophantine fuzzy N-soft set and define its operations. 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. 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. We introduced the novel concept of m-polar Diophantine fuzzy N-soft sets (MPDFNS sets).