Fuzzy submonoids, fuzzy preorders and quasi-metrics
Let L be a residuated lattice. Then, given a monoid M, we define a Galois connection from the lattice of the compatible L-preorders in M and the lattice of L-submonoids of M. Given a set S we define a Galois connection between the lattice of the L-preorders in S and the lattice of L-submonoids of the monoid (S-S, o, i). A link with the notion of quasi-metric is also established. (C) 2006 Elsevier B.V. All rights reserved.
residuated lattices fuzzy monoids fuzzy orders similarities quasi-metric spaces