Regular left-continuous t-norms
|Title:||Regular left-continuous t-norms|
This paper is on left-continuous (l.c.) t-norms. A l.-c. t-norm is called regular if the number of discontinuity points of the vertical cuts is globally bounded, and if the intersection of the identity line and the vertical cut belonging to some point a depends on a in a particularly simple manner. The t-norm algebras based on regular l.-c. t-norms generate the variety of MTL-algebras.
With each regular l.-c. t-norm, we associate certain characteristic data, which in particular describes a finite number of constituents, each of which belongs to one out of six different types. The characteristic data determines the t-norm to a high extent; most of the commonly known t-norms are actually completely determined by it. -- The main tool used are algebras of commuting functions from the real unit interval to itself.