Jia-Bao Liu, Shahbaz Ali*, Muhammad Khalid Mahmood and Muhammad Haris Mateen Pages 1 - 11 ( 11 )
Introduction: In this paper, we present a novel hybrid model m-polar Diophantine fuzzy N-soft set and define operations on it.
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 Nsoft sets and examine few outcomes which do not hold in Pythagorean fuzzy N-soft sets complements unlike to crisp set. We further discuss about (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 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 overcome drawbacks of existing models which are to be generalized.
Conclusion: We introduced novel concept of m-polar Diophantine fuzzy N-soft sets (MPDFNS sets).
m-polar Diophantine fuzzy N-soft sets, m-polar diophantine fuzzy N-soft set complements, (α, β, γ)-cut of mpolar diophantine fuzzy N-soft set
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, Department of Mathematics, Khawaja Fareed University of Engineering & Information Technology, 64200, Rahim Yar Kahn, Department of Mathematics, University of the Punjab Lahore 54590, Department of Mathematics, University of the Punjab Lahore 54590, Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, 64200, Rahim Yar Khan