University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065414420170830TOPOLOGICAL SIMILARITY OF L-RELATIONS99115332810.22111/ijfs.2017.3328ENJingHaoCollege of Mathematics and Information Science, Henan University of
Economics and Law, Zhengzhou, 450000, ChinaShashaHuangCollege of Mathematics and Information, North China University of
Water Resources and Electric Power, Zhengzhou, 450045, ChinaJournal Article20160603$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing the<br />equivalence relations to $L$-relations. The topological structures induced by<br />$L$-fuzzy rough sets have opened up the way for applications of topological facts<br />and methods in granular computing. In this paper, we firstly prove that<br />each arbitrary $L$-relation can generate an Alexandrov $L$-topology.<br />Based on this fact, we introduce the topological similarity of $L$-relations,<br />denote it by T-similarity, and we give intuitive characterization of<br />T-similarity. Then we introduce the variations of a given $L$-relation and<br />investigate the relationship among them. Moreover, we prove that each<br />$L$-relation is uniquely topological similar to an $L$-preorder. Finally,<br />we investigate the related algebraic structures of different sets of<br />$L$-relations on the universe.http://ijfs.usb.ac.ir/article_3328_9d91e0d6e83d4532a68b2d14d8756c97.pdf