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Journal of Intelligent Systems

Editor-in-Chief: Fleyeh, Hasan

CiteScore 2018: 1.03

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Volume 25, Issue 2


Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras

Abdelaziz Amroune
  • Faculty of Mathematics and Informatics, Department of Mathematics, M’sila University, P.O. Box 166, Ichbilia, M’sila 28000, Algeria
  • Other articles by this author:
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/ Lemnaouar Zedam
  • Corresponding author
  • Faculty of Mathematics and Informatics, Department of Mathematics, M’sila University, P.O. Box 166, Ichbilia, M’sila 28000, Algeria
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  • Other articles by this author:
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/ Bijan Davvaz
Published Online: 2015-02-06 | DOI: https://doi.org/10.1515/jisys-2014-0096


The aim of this article is to develop a representation theory of interval-valued Łukasiewicz–Moisil algebras; the concept of interval fuzzy sets involves the role that the notion of field of sets plays for the representation of Boolean algebras. This theory provides both a semantic interpretation of a Łukasiewicz interval-valued logic and a logical basis for the interval fuzzy sets theory.

Keywords: Fuzzy set; lattice; interval-valued Łukasiewicz–Moisil algebra; fuzzy algebra

MSC: 03E72; 03G20


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About the article

Received: 2014-05-15

Published Online: 2015-02-06

Published in Print: 2016-04-01

Citation Information: Journal of Intelligent Systems, Volume 25, Issue 2, Pages 99–106, ISSN (Online) 2191-026X, ISSN (Print) 0334-1860, DOI: https://doi.org/10.1515/jisys-2014-0096.

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