Research Of Multi-granulation Covering Rough Intuitionistic Fuzzy Set Models

In order to deal with vague,inexact and uncertain knowledge in information systems,a rough set model was proposed by Pawlak.The theory of rough sets has had extensive and profound influences since it was proposed.Fuzzy sets were proposed by Zadeh in order to describe the concepts of vagueness and fuzziness.On the basis of Zadeh's fuzzy sets,Atanassov developed the concept of intuitionistic fuzzy sets(IFS).The theory interprets the fuzziness concept with “neither this nor that” and “both this and that” by presenting three notions of the membership degree,non-membership degree and hesitation degree,respectively.In fact,rough sets and fuzzy sets,which may be simultaneously present in a given application,do not mean the same role in knowledge representation.What is more,they are not the opposite theories for imperfection,accuracy and vagueness.The combination of the two theories is natural,but not from a formal point of view.In the fusion and innovation of the two theories,Dubois firstly combined them into rough fuzzy sets and fuzzy rough sets,which raised the attentions of many scholars.In recent years,the study of rough sets,neighborhood and multi-granularity rough sets rough sets has attracted the attention of many scholars.The development of these forms of rough sets is a new research direction.At present,the combinations of rough sets and intuitionistic fuzzy sets,as well as the combination of neighborhood rough sets and intuitionistic fuzzy sets,have few research results from the point of view of granularity.These studies have certain significance.Therefore,based on the theory of cover theory,this paper combined rough sets,neighborhood rough sets with intuitionistic fuzzy sets.This paper extends the cover rough intuitionistic fuzzy sets from the point of view of granularity,some models are constructed.Their properties are discussed and illustrated with examples.The innovation of this paper is as follows:Firstly,the concept of fuzzy covering-based rough membership and non-membership are defined based on the rough sets theory,intuitionistic fuzzy sets theory and covering theory.The relationships are taken into fully account that between the memberships and non-memberships of the elements themselves and the minimal descriptions of elements.Then a new models are established,which is covering-based rough intuitionistic fuzzy sets model and their properties are proved.At the same time,a new similarity measure formula is proposed in the intuitionistic fuzzy sets,and we used as an example to illustrate itsapplication.Secondly,from the view of granularity,we propose a novel concept which is the minimal description based on multi-granulation.Fuzzy multi-granulation covering rough membership and non-membership degrees are defined.Two models are established.Some properties of these models are proved and demonstrated by some examples.Thirdly,the combination of the multi-granulation neighborhood rough set and the intuitionistic fuzzy set is further researched.The concepts of the intuitionistic fuzzy covering-based rough membership and non-membership are defined for dealing with the heterogeneous data including categorical attributes and numerical attributes.A multi-granulation neighborhood rough intuitionistic fuzzy set model is established based on double granulate criterion which are different attribute sets sequence and different neighborhood radii.The properties of multi-granulation neighborhood rough intuitionistic fuzzy set are discussed.The approximate set of the optimistic and pessimistic multi-granulation neighborhood rough intuitionistic fuzzy sets are constructed and their properties are discussed.These models are illustrated with examples.