How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number...

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Autores principales: Bazhenov, Nikolay, Mustafa, Manat, Ospichev, Sergei, San Mauro, Luca
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2023
Materias:
Original Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9902436/
https://www.ncbi.nlm.nih.gov/pubmed/36777490
http://dx.doi.org/10.1007/s11229-023-04056-y
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author Bazhenov, Nikolay
Mustafa, Manat
Ospichev, Sergei
San Mauro, Luca
author_facet Bazhenov, Nikolay
Mustafa, Manat
Ospichev, Sergei
San Mauro, Luca
author_sort Bazhenov, Nikolay
collection PubMed
description Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy.
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spelling pubmed-99024362023-02-08 How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy Bazhenov, Nikolay Mustafa, Manat Ospichev, Sergei San Mauro, Luca Synthese Original Research Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. Springer Netherlands 2023-02-06 2023 /pmc/articles/PMC9902436/ /pubmed/36777490 http://dx.doi.org/10.1007/s11229-023-04056-y Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Research
Bazhenov, Nikolay
Mustafa, Manat
Ospichev, Sergei
San Mauro, Luca
How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
title How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
title_full How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
title_fullStr How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
title_full_unstemmed How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
title_short How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
title_sort how to approximate fuzzy sets: mind-changes and the ershov hierarchy
topic Original Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9902436/
https://www.ncbi.nlm.nih.gov/pubmed/36777490
http://dx.doi.org/10.1007/s11229-023-04056-y
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