Closure operators constructed by logical operations on bounded lattices

Abstract

In this paper, closure operators obtained from functions having some properties on bounded lattices are defined. By this way, it is aimed to generalize the notions T and U-closure operators obtained from t-norms and uninorms, respectively. The relationships between the closure operators obtained from functions and their conjugacies (dual functions) are determined. In special cases, the closure operators from implications making closure operators from R-, (S,N)-, QL- implications are determined. Also, the closures of the sets according to the closure operators from implications are studied. The orders obtained from closure operators are introduced, and the properties are discussed.