Erratum to „State operators on generalizations of fuzzy structures“ [Fuzzy Sets Syst. 187 (2012) 58–76].

Abstract

Recently, the authors characterized in Dvurečenskij et al. (2012) [1] subdirectly irreducible Rℓ-monoids with a faithful state operator. Unfortunately, the proof of one of the main theorems (Theorem 4.11) has a gap because we have used a property holding only for commutative Rℓ-monoids as we show. We now present counterexamples and a correct proof.