Attribute Reductions Of Two Inconsistent Generalized Fuzzy Decision Information Systems

Fuzzy sets and rough sets have played an important role in dealing with uncertainty problems in the field of artificial intelligence.Pythagorean fuzzy sets and hesitant fuzzy sets,as extensions of classical fuzzy sets,can solve more complex realworld problems.Meanwhile,using rough approximation operators from generalized fuzzy decision information systems,the attribute reduction has been a popular area of research in pattern recognition.Therefore,attribute reduction algorithms have been proposed by different methods in the Pythagorean fuzzy decision information systems and hesitant fuzzy decision information systems,respectively.The main content of this article is as follows:(1)Attribute reduction algorithms of inconsistent Pythagorean fuzzy decision information systems based on dominance relation are discussed.Firstly,the equivalence relation that forms the quotient set is generalized to a dominance relation,thus dominance covering sets,stripped dominance covering sets,D-stripped dominance covering sets of Pythagorean fuzzy decision information systems are given.Then the positive region and D-stripped dominance covering sets are used to reduce the Pythagorean fuzzy decision information systems.Finally,the attribute reduction algorithms are compared with other attribute reduction algorithms,and the effectiveness of the proposed algorithms are verified.(2)Attribute reduction algorithms of inconsistent hesitant fuzzy decision information systems based on hypergraphs are discussed.Firstly,a decision system with binary relations is converted into a hesitant fuzzy decision information system using a hesitant fuzzy relation.Next,by using a pair of dual score functions of hesitant fuzzy sets,a novel hesitant fuzzy rough approximation operator based on dual score functions is proposed.Since decision makers have different attitudes,four hesitant fuzzy rough approximation operators are obtained.Lower approximation distribution consistent sets and lower approximation distribution reductions are obtained by using the four newly arrived hesitant fuzzy rough approximation operators.Moreover,by using a fuzzy granule of hesitant fuzzy sets,an attribute reduction approach based on the hesitant fuzzy rough sets is constructed.Finally,it is discovered that finding the lower approximation distribution reductions of a hesitant fuzzy decision system is equivalent to finding the minimal transversals of its induced hypergraph.Therefore,an improved algorithm to find all lower approximation distribution reductions is proposed.The hybrid data of Hepatitis C Virus is used for data analyses to reflect the effectiveness of the proposed algorithm.