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

Amroune Abdelaziz; Zedam Lemnaouar; Davvaz Bijan

doi:10.1515/jisys-2014-0096

Journal of Intelligent Systems (Apr 2016)

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

Amroune Abdelaziz,
Zedam Lemnaouar,
Davvaz Bijan

Affiliations

Amroune Abdelaziz: Faculty of Mathematics and Informatics, Department of Mathematics, M’sila University, P.O. Box 166, Ichbilia, M’sila 28000, Algeria
Zedam Lemnaouar: Faculty of Mathematics and Informatics, Department of Mathematics, M’sila University, P.O. Box 166, Ichbilia, M’sila 28000, Algeria
Davvaz Bijan: Department of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, Iran

DOI: https://doi.org/10.1515/jisys-2014-0096
Journal volume & issue: Vol. 25, no. 2
pp. 99 – 106

Abstract

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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.

Published in Journal of Intelligent Systems

ISSN: 0334-1860 (Print); 2191-026X (Online)
Publisher: De Gruyter
Country of publisher: Poland
LCC subjects: Science: Mathematics: Instruments and machines: Electronic computers. Computer science
Website: https://www.degruyter.com/view/journals/jisys/jisys-overview.xml

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