TOPOLOGICAL SIMILARITY OF L-RELATIONS

Document Type: Research Paper

Authors

1 College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450000, China

2 College of Mathematics and Information, North China University of Water Resources and Electric Power, Zhengzhou, 450045, China

Abstract

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing the
equivalence relations to $L$-relations. The topological structures induced by
$L$-fuzzy rough sets have opened up the way for applications of topological facts
and methods in granular computing. In this paper, we firstly prove that
each 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 of
T-similarity. Then we introduce the variations of a given $L$-relation and
investigate 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.

Keywords


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