Category theory for computing science
Category theory for computing science
Categories, types, and structures: an introduction to category theory for the working computer scientist
Categories and computer science
Categories and computer science
Triangular norms on product lattices
Fuzzy Sets and Systems - Special issue on triangular norms
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Pseudo-t-norms and implication operators on a complete Brouwerian lattice
Fuzzy Sets and Systems - Possibility theory and fuzzy logic
Automorphisms, negations and implication operators
Fuzzy Sets and Systems - Implication operators
The best interval representations of t-norms and automorphisms
Fuzzy Sets and Systems
Advances and challenges in interval-valued fuzzy logic
Fuzzy Sets and Systems
Extension of fuzzy logic operators defined on bounded lattices via retractions
Computers & Mathematics with Applications
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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 generalizations of automorphisms are the morphisms of the category. We will prove that, this category is an interval category, which roughly means that it is a Cartesian category with an interval covariant functor.