A general method for constructing left-continuous t-norms

✍ Scribed by Sándor Jenei; Franco Montagna

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 775 KB
• Volume: 136
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(02)00275-0

✦ Synopsis

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 -MTL of HÃ ajek.