Abstract
A new method for constructing (left-continuous) t-norms is introduced and analyzed in this paper. We shall construct via embedding a left-continuous t-norm from any countable residuated totally and densely ordered commutative integral monoid. Moreover, we can construct a left-continuous t-norm from any countable, totally ordered, commutative integral monoid which is not necessarily densely ordered and residuated. A special case, the embedding of such monoids on lexicographic product spaces is investigated in detail, and several examples are demonstrated. The results shed some light to Chang's MV-algebra, to a recently proposed ‘extraordinary’ t-norm, and to the standard semantics of the recently introduced logic Π- MTL of Hájek.
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