Erratum to „State operators on generalizations of fuzzy structures“ [Fuzzy Sets Syst. 187 (2012) 58–76].
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Elsevier
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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.
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algebras of fuzzy logics, residuated lattice, state operator, faithful state operator, subdirectly irreducible algebra
Citation
Fuzzy Sets and Systems. 2012, vol. 194, issue 1, p. 97-99.