The \(\alpha\)-embedded and \(A\)'s fuzzy decomposition theorems
The paper deals with decompositions of fuzzy sets based on the concept of \(\alpha\)-cuts. The attention is focused to several questions, namely if a fuzzy set can be decomposed into series of \(\alpha\)-cuts or into several sets derived from these \(\alpha\)-cuts and called their \(\alpha\)-embedded sets. The main results are formulated in several versions of fuzzy union-decomposition theorems and fuzzy intersection-decomposition theorems. The relation between these theorems is investigated as well.
scientific article; zbMATH DE number 1423478
scientific article