Characterizing closure systems in the graded setting - CMMSE

Abstract

Closure systems play a major role in both pure and applied mathematics. This paperpresents an extension of the notion of closure system, which is done adapting theidea of meet-subsemilattice to a complete fuzzy lattice. This extension is carried outon two levels, first as crisp sets and then as fuzzy sets. In both cases, the one-to-onerelations between closure operators and closure systems that hold in the classicalcase are extended properly to this framework. Furthermore, a novel characterizationfor a closure system is established.