Fuzzy submonoids, fuzzy preorders and quasi-metrics

er is an extended abstract of my paper [12] published in Fuzzy Set and Systems. We start from a residuated lattice L and a monoid M, and 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 (SS, , i). A link with the notion of quasi-metric is also established. Keywords. Fuzzy monoids, fuzzy orders, similarities, quasi-metric spaces, residuated lattices.

• Type: Journal
• Year: 2006
• Where: FSS
• Authors: Giangiacomo Gerla
• Keywords: FSS 2006, Fuzzy Set, Galois Connection, Residuated Lattice