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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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Detalles Bibliográficos
Autores principales: Bazhenov, Nikolay, Mustafa, Manat, Ospichev, Sergei, San Mauro, Luca
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2023
Materias:
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
Descripción
Sumario: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.