Set functors, L-fuzzy set categories, and generalized terms

✍ Scribed by P. Eklund; M.A. Galán; J. Medina; M. Ojeda-Aciego; A. Valverde

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 925 KB
• Volume: 43
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(01)00314-5

✦ Synopsis

this work, we generalize previous constructions of fuzzy set categories, introduced in [I], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the Lfuzey categories, which are proven to be rational. In the final part of the paper, the L-fuzzy functors given by the extension principles are provided with a structure of monad which is used, together with the functorial definition of the term monad, to provide monad compositions as a basis for a notion of genera&d terms. @ 2002 Elsevier Science Ltd. All rights reserved.

Keywords-Extension

principles, General&d terms, Monad compositions.

'The condition A(r) > 0 can be neglected in the maximal extension principles, but not in the minimal ones. For uniformity, we have used a similar representation for both.