Abstract
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.
Original language | English |
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Article number | 55 |
Journal | Synthese |
Volume | 201 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2023 |
Keywords
- Computability theory
- Ershov Hierarchy
- Fuzzy set
- n-Computably enumerable set
ASJC Scopus subject areas
- Philosophy
- General Social Sciences