Research On Soft Set Theory Under Pythagorean Fuzzy Environment

In real life,the uncertainty can be seen everywhere.The traditional mathematical methods are difficult to fulfil the practical requirements when facing the uncertainty.Therefore,many uncertainty theories have been come out one after another,such as fuzzy set,intuitionistic fuzzy set,Pythagorean fuzzy set and soft set.As a new mathematical tool for dealing with uncertainty,soft set theory has attracted the researchers in various fields,and many fruitful results have emerged.In view of this,in this paper the soft set theory and its extension theory are introduced into Pythagorean fuzzy environment to research on the theory and application.The details are as follows:1.By quantifying the attribute uncertainties,a generalized Pythagorean fuzzy soft set model is constructed based on the Pythagorean fuzzy soft set model,and the basic operations and properties of this model are also discussed.Secondly,a similarity measure method of this model is established,and an example is provided to illustrate the effectiveness and practicability of the method.2.The operations of this model such as the generalized intersection,the narrow intersection,AND and OR operators are given,and their basic properties are also investigated.The algebraic structures of the model are further explored.First,three lattice structures of the generalized Pythagorean fuzzy soft set are constructed.Then it is also proved that the three lattice structures are soft algebraic structures.Finally,we establish three complemented distributive lattices which are also called Boolean lattices.3.By introducing the N-soft set into Pythagorean fuzzy environment,we present a novel framework for the study of Pythagorean fuzzy N-soft sets.Then,the operations of this model such as the weak complement,generalized intersection and narrow intersection are first defined.Finally,two decision algorithms are established based on Pythagorean fuzzy N-soft sets model.A practical example is also provided to illustrate the validity and practicality of Pythagorean fuzzy N-soft sets with multi-attribute group decision-making problems.