How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
Bazhenov N. Mustafa M. Ospichev S. San Mauro L.
February 2023Springer Science and Business Media B.V.
Synthese
2023#201Issue 2
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.
Computability theory , Ershov Hierarchy , Fuzzy set , n-Computably enumerable set
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Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., Novosibirsk, 630090, Russian Federation
Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, 53 Qabanbaybatyr Avenue, Astana, 010000, Kazakhstan
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10/104, Vienna, 1040, Austria
Sobolev Institute of Mathematics
Department of Mathematics
Institute of Discrete Mathematics and Geometry
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