Fuzzy Rough Sets Based On The Generalized Fuzzy Partitions

This paper defines the concepts of fuzzy granulars andσ_L fuzzy granulars based on fuzzy T -similar relations,and develops their basic properties;we discuss the relationships between the properties of the fuzzy granulars and fuzzy T -similar relations,that ofσ_L fuzzy granulars fuzzy and T -similar relations.Later on,generalized fuzzy partitions andσfuzzy partitions are given,and fuzzy rough sets described by the fuzzy granulars andσ_L fuzzy granulars are firstly constructed,which are proved that the fuzzy rough sets based on the on generalized fuzzy partitions andσ_L fuzzy partitions related to the ones that proposed by membership functions closely.Finally,the concepts of relative reduction and relative kernel are proposed.An example is employed to illustrate the application of the relative reduction and relative kernel of the fuzzy rough sets.