Publication Date
8-1-2023
Abstract
For normalized fuzzy sets, intersection is, in general, not normalized. So, if we want to limit ourselves to normalized fuzzy sets, we need to normalize the intersection. It is known that for algebraic product, the normalized intersection is associative, and that for many other "and"-operations (t-norms), normalized intersection is not associative. In this paper, we prove that algebraic product is the only "and"-operation (even the only "and-like" operation) for which normalized intersection is associative.
Comments
Technical Report: UTEP-CS-23-49a