Abstract
BL algebras were introduced by Hájek as algebraic structures for his Basic Logic, starting from continuous t-norms on [0,1]. MV algebras, product algebras and Gödel algebras are particular cases of BL algebras. On the other hand, the pseudo-MV algebras extend the MV-algebras in the same way in which the arbitrary l-groups extend the abelian l-groups. We have generalized the BL algebras and pseudo-MV algebras, introducing the pseudo-BL algebras. In this paper we introduce weak-BL algebras and weak-pseudo-BL algebras. We also introduce non-commutative t-norms (we call them pseudo-t-norms) and use them in constructing pseudo-BL algebras and weak-pseudo-BL algebras.
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Flondor, P., Georgescu, G. & Iorgulescu, A. Pseudo-t-norms and pseudo-BL algebras. Soft Computing 5, 355–371 (2001). https://doi.org/10.1007/s005000100137
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DOI: https://doi.org/10.1007/s005000100137