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

Nikolay Bazhenov, Manat Mustafa, Sergei Ospichev, Luca San Mauro

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number55
Issue number2
Publication statusPublished - Feb 2023


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

ASJC Scopus subject areas

  • Philosophy
  • General Social Sciences


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