Left-continuous t-norms as Functional Algebras
نویسنده
چکیده
With a left-continuous t-norm ̄, we may associate the set of its vertical cuts, namely, the set F of functions fa : [0, 1] → [0, 1], x 7→ x ̄ a. Endowed with the pointwise order, with the functional composition, with the constant 0 function and with the identity function, F is an algebra which is isomorphic to ([0, 1];≤, ̄, 0, 1). We characterize the functional algebras arising in this way from left-continuous t-norms; the key property is that every two functions commute. On the basis of this approach, we describe a subclass of the left-continuous tnorms in a unified way. This subclass comprises most left-continuous t-norms discussed in the literature.
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