Mathematical Institute of the Serbian Academy of Sciences and Arts
|Title:||Fuzzy logic and enriched categories||Journal:||Iranian Journal of Fuzzy Systems||Volume:||18||Issue:||3||First page:||1||Last page:||11||Issue Date:||1-May-2021||Rank:||~M21a||ISSN:||1735-0654||DOI:||10.22111/ijfs.2021.6077||Abstract:||
We consider a category C enriched over the segment [0, 1] whose hom-objects are real numbers from [0, 1]. For a suitably defined function ˆv assigning to each formula φ some object of C, the hom-object C(ˆv(φ), ˆv(ψ)) represents the degree of derivability of ψ from φ. We reformulate completeness result for intuitionistic propositional logic, as well as Hájek’s completeness results concerning the product, Gödel and łLukasiewicz fuzzy logic in the context of enriched category theory.
|Keywords:||Bicartesian closed V-enriched category | Gödel fuzzy logic | Product fuzzy logic | Self-enriched category | T-norm | łLukasiewicz fuzzy logic||Publisher:||University of Sistan and Baluchestan|
Show full item record
checked on Oct 3, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.