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

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

Journal

Synthese
ISSN: 0039-7857 , E-ISSN: 1573-0964

Output data

Year: 2023, Volume: 201, Number: 2, Article number : 55, Pages count : 25 DOI: 10.1007/s11229-023-04056-y

Tags

Fuzzy set · Computability theory · n-Computably enumerable set · Ershov Hierarchy

Authors

Bazhenov Nikolay ¹ , Mustafa Manat ² , Ospichev Sergei ¹ , San Mauro Luca ³

Affiliations

1	Sobolev Institute of Mathematics
2	Department of Mathematics, School of Sciences and Humanities, Nazarbayev University
3	nstitute of Discrete Mathematics and Geometry, Vienna University of Technology

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0011

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.

Bazhenov N. , Mustafa M. , Ospichev S. , San Mauro L.
How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
Synthese. 2023. V.201. N2. 55 :1-25. DOI: 10.1007/s11229-023-04056-y WOS Scopus РИНЦ OpenAlex

Submitted:	Jan 30, 2022
Accepted:	Jan 17, 2023
Published print:	Feb 6, 2023
Published online:	Feb 6, 2023

Web of science:	WOS:000926688600002
Scopus:	2-s2.0-85147589000
Elibrary:	60997886
OpenAlex:	W4319317082

Пока нет цитирований