Geodesic
Equivalence among L-closure (interior) operators, L-closure (interior) systems and L-enclosed (internal) relations
Filomat, Tome 36 (2022) no. 3, p. 979

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DOI

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
DOI : 10.2298/FIL2203979Z
Classification : 03E72, 52A01, 54A05
Keywords: L-closure operator, L-closure system, L-enclosed relation, L-interior operator, L-interior system, L-internal relation 
Fangfang Zhao; Bin Pang. Equivalence among L-closure (interior) operators, L-closure (interior) systems and L-enclosed (internal) relations. Filomat, Tome 36 (2022) no. 3, p. 979 . doi: 10.2298/FIL2203979Z
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     title = {Equivalence among {L-closure} (interior) operators, {L-closure} (interior) systems and {L-enclosed} (internal) relations},
     journal = {Filomat},
     pages = {979 },
     year = {2022},
     volume = {36},
     number = {3},
     doi = {10.2298/FIL2203979Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2203979Z/}
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