Irreducibility in algebraic fuzzy systems
A general theory of algebraic fuzzy systems has been developed by the authors in the paper reviewed above (see Zbl 0732.08002). This paper continues this work; the main results concern irreducibility in algebraic fuzzy systems. The authors propose an important notion, prime fuzzy \({\mathcal S}\)-subsets of a nonempty set X having truth values in a complete Brouwerian lattice L, which is determined by pairs (p,\(\alpha\)), where p is a prime element of \({\mathcal S}\) and \(\alpha\) is an irreducible element of L. The main result is that the space of all prime fuzzy \({\mathcal S}\)- subsets of X together with its hull-kernel topology is homeomorphic to the product of the spaces of prime elements of \({\mathcal S}\) and of irreducible elements of L, equipped with hull-kernel topologies.
scientific article; zbMATH DE number 4210217