Closure Structures as fixed points of some Galois connections.

Abstract

The starting point of this work is a published paper where the fuzzy powerset of a fuzzy lattice A, the set of isotone mappings on A and the set of isotone total relations on A were proved to be related by three fuzzy Galois connections such that fuzzy closure systems, fuzzy closure operators and the so called strong fuzzy closure relations are fixed points. The final part of that paper studied the commutativity of the diagrams formed by these mappings.