A Generalized Class of T-norms From a Categorical Point of View

Triangular norms or t-norms, in short, and automorphisms are very useful to fuzzy logics in the narrow sense. However, these notions are usually limited to the set [0,1]. In this paper we will consider a generalization of the t-norm notion for arbitrary bounded lattices as a category, where these ge...

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Bibliographic Details
Main Authors: Bedregal, B.C., Santos, H.S., Callejas-Bedregal, R.
Format: Conference Proceeding
Language:English
Subjects:
Boolean algebra
Extraterrestrial measurements
Fuzzy logic
Informatics
Lattices
Mathematics
Proposals
Set theory
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Summary:Triangular norms or t-norms, in short, and automorphisms are very useful to fuzzy logics in the narrow sense. However, these notions are usually limited to the set [0,1]. In this paper we will consider a generalization of the t-norm notion for arbitrary bounded lattices as a category, where these generalized t-norms are the objects, and a generalization of automorphism notion as the morphism of the category. We will prove that, this category is Cartesian and a subcategory of it is Cartesian closed. We show that the usual interval t-norms can be seen as a covariant functor for that category.
ISSN:1098-7584
DOI:10.1109/FUZZY.2007.4295530