| In this paper,the concepts of D_α- continuity,D_α- convergence,D_α- stratified connectedness,I_r- countability,D_α- separations are discussed based on D_α- closed set and I_r- open set,and to study the relationships between rough sets and L-fuzzy topology. The major contents and research results are listed as follows:1,In L-fuzzy topological space, the concepts of D_α- continuity,strong D_α- continuity,D_α- closed order homomorphism,D_α- continuity of molecular nets are defined based on D_α- closed sets;the D_α- adhesive point,D_α- limit point,D_α- cluster point with respect to a molecular net (ideal)are defined based on D_α- closed sets;the D_α- Stratified connectedness is defined based on D_α- closed sets, and some basic properties are discussed. Moreover , some properties are compared among D_α- connectedness and others. The characteristics of the concepts are systematically discussed.2,The concepts of the first and the second I_r- countably space are defined in L-fuzzy stratified topological spaces. Some basic properties of them are respectively given. The relationships and some applications of them are discussed. Both of the first and the second I_r- countability are hereditary property, countable multiplicative property and invariable property under D_α- order homomorphism of homeomorphism is proved. In L-fuzzy stratified topological spaces,the concepts of the quasi I_r- Lindel o.. fproperty and D_α- Ti separations are defined based on D_α- closed sets. The properties of the concepts are systematically discussed. Therefore, the main results of the quasi I_r- Lindel o.. fproperty and Ti ? separations in LF topology are preserved in much wider LF stratified topological spaces. such as closely hereditary,weakly topology invariability and good extension.3,In this paper the theory of covering generalized rough sets are studied with L-fuzzy topology. The relative interior and closure operators are defined in L-fuzzy topological space and their basic properties are discussed. The major research results are listed as follows: The properties of relative interior and closure operators,The necessary and sufficient condition for relative interior and relative closure generated by two subbases of the same topological space ,to be the same ,respectively,The axiomatization of relative interior and closure operators. These results can be considered as fundamental theory of rough sets and L-fuzzy topology. |
