Cut systems in sets with similarity relations
Fuzzy sets with values in a complete lattice \(L\) can be defined either by means of membership functions, or, equivalently, by means of nested systems of \(\alpha\)-cuts. This paper is focused on finding some analogies between the second approach and some nested systems of subsets defined in sets with similarity relations. Special \(f\)-cut systems are introduced and their properties and category-theoretic isomorphic objects are discussed. Moreover, a first-order fuzzy logic interpretations in cut systems are discussed, proving, among others, some relationships between classical interpretations in sets with similarity relations and interpretations using nested systems.
fuzzy sets in sets with similarity relations
scientific article; zbMATH DE number 5843060