Hesitant Pythagorean Fuzzy Rough Sets And Their Applications In Multi-attribute Decision-making

Rough sets originated by Pawlak in 1982 is viewed as an effective tool for imprecise,uncertainty data analysis?rule extraction?machine learning and so on.To apply this model better in practice,substantial number of researchers generalized this model by generalizing the single universe to two universe,the equivalence relation to the general relation,one relation to multiple relations,the crisp concept to fuzzy concept.Moreover,they developed the generalized model by considering the combination of it and fuzzy set?intuitionistic fuzzy set?Pythagorean fuzzy set?hesitant fuzzy set and so on.Due to the complexity?uncertainty and hesitancy,Liang and Xu originated the hesitant Pythagorean fuzzy set(HPFS).Under the hesitant Pythagorean circumstance,it allows the Pythagorean membership and Pythagorean non-membership have several different values.It fully considers the hesitancy of Pythagorean membership and Pythagorean non-membership.To cope with the uncertainty problems that we confront in our life,in this paper,by integrating HPFS with rough set,we firstly put forward the single granulation hesitant Pythagorean fuzzy rough sets,we further grope for its properties and examine the monotonicity of hesitant Pythagorean fuzzy lower and upper approximation operators w.r.t.the hesitant Pythagorean fuzzy relations.Then,in consideration of the multigranulation framework,we originate two types of multigranulation hesitant Pythagorean fuzzy rough sets,called the optimistic and the pessimistic multigranulation hesitant Pythagorean fuzzy rough sets,respectively.We further grope their properties and build the relation between the multigranulation hesitant Pythagorean fuzzy rough sets and single granulation hesitant Pythagorean fuzzy rough sets.Moreover,the monotonicity of multigranulation hesitant Pythagorean fuzzy lower and upper approximation operators w.r.t.the hesitant Pythagorean fuzzy relations are discussed,and the relationship between two types of multigranulation hesitant Pythagorean fuzzy rough sets is established subsequently.Ultimately,we provide an application model?an algorithm?and an example to expound the availability about the multigranulation hesitant Pythagorean fuzzy rough sets in multi-attribute decision making.