Abstract We study (strictly) join irreducible varieties in the lattice of subvarieties residuated lattices. explore connections with well-connected algebras and suitable generalizations, focusing particular on representable varieties. Moreover, we find weakened notions Halldén completeness that characterize irreducibility. strictly basic hoops use generalized rotation construction to $\mathsf{M...

It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of posit...

The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...