Abstract
This paper investigates the topological structures of L-fuzzy rough sets. In particular, the family of lower (resp. upper) sets with respect to an arbitrary L-fuzzy relation is proved to be an Alexandrov L-fuzzy topology. Lower and upper similarity sets of L-fuzzy relations are studied with the transitive closure of L-fuzzy relation to investigate L-fuzzy relations inducing the same Alexandrov L-fuzzy topology by lower and upper sets, respectively. Moreover, the transitive subsets of lower and upper similarity sets of the same L-fuzzy relation coincide with each other, which are shown to be complete distributive lattices.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.