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...

Descripción completa

Detalles Bibliográficos
Publicado en:Synthese Vol. 201; no. 2; pp. 1 - 26
Autores principales: Bazhenov, Nikolay, Mustafa, Manat, Ospichev, Sergei, San Mauro, Luca
Formato: Artículo
Publicado: Springer Nature Feb2023
Acceso en línea:Ver este registro en EBSCOhost
fields @attributes:
  recordID: 1
pdfLink:
plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=162301118&site=ehost-live
header:
  @attributes:
    shortDbName: hlh
    uiTerm: 162301118
    longDbName: Humanities International Complete
    uiTag: AN
  controlInfo:
    bkinfo:
    jinfo:
      jid:
        00397857
        4LI
      jtl: Synthese
      issn: 00397857
      maglogo: N
    pubinfo:
      dt: Feb2023
      vid: 201
      iid: 2
      pid: 237
      pub: Springer Nature
    artinfo:
      ui:
        162301118
        10.1007/s11229-023-04056-y
      ppf: 1
      ppct: 25
      formats:
        fmt:
          – @attributes:
              type: T
          – @attributes:
              type: P
              size: 415KB
      tig:
        atl: How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy.
      aug:
        au:
          Bazhenov, Nikolay
          Mustafa, Manat
          Ospichev, Sergei
          San Mauro, Luca
        affil:
          Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090, Novosibirsk, Russia
          Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, 53 Qabanbaybatyr Avenue, 010000, Astana, Kazakhstan
          Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10/104, 1040, Vienna, Austria
      sug:
      keyword:
        03D55
        03E72
        Computability theory
        Ershov Hierarchy
        Fuzzy set
        n-Computably enumerable set
      ab: 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.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
    refInfo:
    copyright:
      @attributes:
        flag: Y
      custom: Synthese is a copyright of Springer, 2023. All Rights Reserved.
      item: Synthese
      holder: Springer Nature
      dt:
        @attributes:
          year: 2023
    holdings:
      @attributes:
        islocal: N