Abstract
In this paper, by integrating Pythagorean fuzzy set with N-soft set, we propose a generalization of N-soft set called the theory of Pythagorean fuzzy N-soft set and explore some of related operations concerning this theory including the weak complement, extended union and intersection, restricted union and intersection. Then two algorithms are introduced to Pythagorean fuzzy N-soft sets for dealing with multi-attribute group decision-making problems. Finally, a practical example is provided to illustrate the validity and practicality of Pythagorean fuzzy N-soft sets in multi-attribute group decision-making problems. Compared with the existing models, we also elaborate the advantages of this model.
Highlights
With the continuous development of society, there exist a large number of fuzzy phenomena in all fields of life
By introducing N -soft set into Pythagorean fuzzy environment, a new hybrid model called Pythagorean fuzzy N -soft set (PFNSS) model is constructed in which the square sum of membership degree and non-membership degree is allowed to be less than to 1
SOME RELATIONSHIPS In the above sections, we introduce N -soft sets into Pythagorean fuzzy environment, and construct a PFNSS model
Summary
With the continuous development of society, there exist a large number of fuzzy phenomena in all fields of life. Majumdar and Samantha [23] proposed a generalized fuzzy soft set on the basis of fuzzy soft set and applied it to decision-making problems. Yang et al [42] proposed the concept of multi-fuzzy soft sets and applied it to decision making problems. Fatimah et al [11] extended soft set under non-binary evaluation environment, proposed a new model called N -soft set (NSS), and explained the importance of ordered grades in practical problems. By introducing N -soft set into Pythagorean fuzzy environment, a new hybrid model called Pythagorean fuzzy N -soft set (PFNSS) model is constructed in which the square sum of membership degree and non-membership degree is allowed to be less than to 1.
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