Intuitionistic Fuzzy Rough Sets And Intuitionistic Fuzzy Multigranulation Covering Rough Sets Based On Intuitionistic Fuzzy Logics

As an extension of the general logical conjunctions,the special case of intu-itionistic fuzzy logical conjunctions has been studied and applied to the study of intuitionistic fuzzy rough sets.However,as a more general case,the relationship between intuitionistic fuzzy logic systems and intuitionistic fuzzy rough sets has not been systematically studied.Based on the above considerations,this paper discusses the intuitionistic fuzzy three-valued logic systems,the intuitionistic fuzzy rough set theory based on intuitionistic fuzzy three-valued logic systems and their interrela?tionships.Firstly,based on the binary logic system and the three-valued logic system,the intuitionistic fuzzy complete lattice logic and intuitionistic fuzzy logic are defined.At the same time,as the generalization of classical multi-granulation rough sets,the multi-granulation hybrid optimistic and hybrid pessimistic rough set models are proposed.Secondly,based on dual triangle norms,the intuitionistic fuzzy rough set models were investigated in this paper.The intuitionistic fuzzy set based on the t-norm on the complete lattice and its arithmetic operations were defined and discussed.The TS membership degree and TS non-membership degree of intuitionistic fuzzy sets of dual triangular norms based on t-norm on the complete lattice were defined and characterized.On the basis of similarity relation based on the t-norm on the complete lattice,intuitionistic fuzzy rough set models on the complete lattice based on the t-norm were defined and studied.Thirdly,by establishing the correspondence between intuitionistic fuzzy rough set-s and three-valued logic,two approximate operators of intuitionistic fuzzy covering rough sets are derived from intuitionistic fuzzy logic propositions.The intuitionistic fuzzy covering rough sets based on intuitionistic fuzzy logic are obtained.Aiming at the multi-granularity intuitionistic fuzzy rough set,two approximation operators of intuitionistic fuzzy multi-granulation covering rough sets are derived from intuition-istic fuzzy logic propositions.The intuitionistic fuzzy multi-granulation covering rough sets based on intuitionistic fuzzy logic are proposed,and their properties are characterized.Finally,we propose the intuitionistic fuzzy multi-granulation the hybrid optimism that optimism contains pessimist and the hybrid pessimist that pessimist contain-s optimism covering rough sets.The intuitionistic fuzzy hybrid multi-granulation that contain intuitionistic fuzzy coverings and intuitionistic fuzzy relations rough sets are investigated,which include intuitionistic fuzzy hybrid multi-granulation op-timistic rough sets,intuitionistic fuzzy hybrid multi-granulation pessimistic rough sets,intuitionistic fuzzy hybrid multi-granulation hybrid optimistic rough sets and intuitionistic fuzzy hybrid multi-granulation hybrid pessimistic rough sets.And an example is given.