Characterizing closure systems in the graded setting - CMMSE
AbstractClosure 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.