Affiliation:
1. Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
Abstract
Closure (interior) operators and closure (interior) systems are important
tools in many mathematical environments. Considering the logical sense of a
complete residuated lattice L, this paper aims to present the concepts of
L-closure (L-interior) operators and L-closure (L-interior) systems by means
of infimums (supremums) of L-families of L-subsets and show their
equivalence in a categorical sense. Also, two types of fuzzy relations
between L-subsets corresponding to L-closure operators and L-interior
operators are proposed, which are called L-enclosed relations and L-internal
relations. It is shown that the resulting categories are isomorphic to that
of L-closure spaces and L-interior spaces, respectively.
Publisher
National Library of Serbia
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