Conjugate Families of Mappings in Pointwise Metric Fuzzy Lattices

Abstract

In this paper some relations among the axioms of pointwise metric for fuzzy lattices introduced by Shi are studied. By means of the conjugate families of mappings, some representation results are presented concerning metric, pseudometric and pseudo-quasi-metric fuzzy lattices. These results reconcile the metric lattice theory generated via concept of neighborhood with the one generated via concept of remote-neighborhood.