Open AccessEquivalence among L-closure (interior) operators, L-closure (interior) systems and L-enclosed (internal) relations
Author(s) -
Fangfang Zhao,
Bin Pang
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2203979z
Subject(s) - closure (psychology) , mathematics , closure operator , equivalence relation , pure mathematics , equivalence (formal languages) , categorical variable , algebra over a field , closed set , statistics , economics , market economy
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.