Tomonoid extensions: the key for the construction of t-norms

摘要

Triangular norms, or t-norms for short, play an important role for the semantics of fuzzy logics. Although an enormous number of examples and a remarkable number of construction methods for this kind of operation has been established, a uniform approach is still outstanding. This paper is devoted to a specific algebraic-geometrical framework within which t-norms, up to isomorphism, can be described systematically. By means of a detailed review of an example case, we show how the approach can be applied to the construction of left-continuous t-norms in a straightforward way.