Results on equality algebras

In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, B...

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Bibliographic Details
Published inInformation sciences Vol. 381; pp. 270 - 282
Main Authors Zebardast, F., Borzooei, R.A., Aaly Kologani, M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2017
Subjects
Algebra
BL-algebra
Boolean-algebra
EQ-algebra
Equality algebra
Equivalence
Fuzzy logic
Hertz-algebra
Heyting-algebra
Hoop-algebra
Lattices
MTL-algebra
MV-algebra
Residuated lattice
Semantics
BL-algebra
Hoop-algebra
Hertz-algebra
Equality algebra
Residuated lattice
Boolean-algebra
Heyting-algebra
MTL-algebra
03G25
EQ-algebra
MV-algebra
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Summary:In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, BL-algebra, MV-algebra, Hertz-algebra, Heyting-algebra, Boolean-algebra, EQ-algebra and hoop-algebra. The aim of this paper is to find that under which conditions, equality algebras are equivalent to these logical algebras.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2016.11.027