TOPOLOGICAL SIMILARITY OF L-RELATIONS

L-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to L-relations. The topological structures induced byL-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary L-relation can generate an Alexandrov L-topology.Based on this fact, we introduce the topological similarity of L-relations,denote it by T-similarity, and we give intuitive characterization ofT-similarity. Then we introduce the variations of a given L-relation andinvestigate the relationship among them. Moreover, we prove that eachL-relation is uniquely topological similar to an L-preorder. Finally,we investigate the related algebraic structures of different sets ofL-relations on the universe.

کلیدواژه ها:

L-fuzzy rough set ، L-relation ، Alexandrov L-topology ، L-preorder ، Topological similarity