Attribute Reductions Of Generalized Fuzzy Rough Sets

Attribute reduction,also known as feature selection,refers to removing redundant attributes from the original attribute set and rataining core attributes.It is one of the main contents of rough set theory and plays an important role in intelligent information processing research.This is because each attribute has different importance to a given data set.Redundant attributes not only occupy storage space,but also interfere with decision making.Therefore,it is necessary to perform attribute reductions before analyzing the data.Attribute reductions can not only effectively eliminate data noise without affecting the final decision making,but also improve the learning efficiency.This paper uses different methods to reduce attributes in Pythagorean fuzzy information systems and hesitant fuzzy information systems.The main contents are as follows:(1)Based on generalized dominance relations,the attribute reduction problem of Pythagorean fuzzy information systems is studied.First,two new dominance relations are defined,and according to the definition of the overall evaluation and the special requirements of individual attributes,Pythagorean fuzzy additive operators are used to aggregate individual attribute values of each object into an overall evaluation,then two generalized dominance rough set models are obtained.Using these two models,the attribute reduction problem of dominance Pythagorean fuzzy systems is studied.Secondly,the parameter ??[0,1]is introduced,the ?dominance relation is defined,the generalized ? dominance rough set model is obtained,and the attribute reduction problem is further studied.Finally,an example is used to illustrate the practicability and effectiveness of the proposed methods.(2)As a generalization of fuzzy sets,a hesitant fuzzy set is composed of several uncertain fuzzy elements with possible values.The evidence theory is an important method to study uncertain knowledge and decision problems,so the evidence theory is combined with the knowledge of hesitant fuzzy sets.First,this paper reviews related properties of hesitant fuzzy sets and upper and lower hesitant fuzzy rough approximation operators.Then using these properties,a probability measure of hesitant fuzzy sets is constructed.And the belief and plausibility functions are studied by using the hesitant fuzzy rough upper and lower approximation operators.Finally,an attribute reduction algorithm is constructed using the belief function,and an example is employed to illustrate the feasibility and validity of the algorithm.