%0 Journal Article
%T TOPOLOGICAL SIMILARITY OF L-RELATIONS
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Hao, Jing
%A Huang, Shasha
%D 2017
%\ 08/30/2017
%V 14
%N 4
%P 99-115
%! TOPOLOGICAL SIMILARITY OF L-RELATIONS
%K $L$-fuzzy rough set
%K $L$-relation
%K Alexandrov $L$-topology
%K $L$-preorder
%K Topological similarity
%R 10.22111/ijfs.2017.3328
%X $L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-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 each$L$-relation is uniquely topological similar to an $L$-preorder. Finally,we investigate the related algebraic structures of different sets of$L$-relations on the universe.
%U http://ijfs.usb.ac.ir/article_3328_9d91e0d6e83d4532a68b2d14d8756c97.pdf