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Soft Computing
Published in: Soft Computing 19/2017

20-08-2016 | Foundations

The decomposition of linearly ordered pseudo-hoops

Author: Rodica Ceterchi

Published in: Soft Computing | Issue 19/2017

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Abstract

We generalize to the non-commutative case a construction of the Hájek decomposition using an equivalence relation on linear pseudo-hoops. Other two equivalence relations are used to obtain the Agliano–Montagna and the Cignoli–Esteva–Godo–Torrens decompositions. The comparability of the three decompositions follows from this construction.
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Footnotes
1
The author’s participation at LATD 2012 was made possible by a travel grant and local support from the organizers.
 
Literature
Ceterchi R (2001) Pseudo–Wajsberg algebras. Mult-Valued Log 6(1–2):67–88 (a special issue dedicated to the memory of Gr. C. Moisil)MathSciNetMATH
Ceterchi R (2012) The Decomposition of linearly ordered pseudo-hoops. In: LATD 2012, 10–14 September 2012, Kanazawa, Ishikawa, Japan
Ceterchi R (2014) A categorical equivalence for a class of product pseudo-hoops. In: Proceedings of the workshop “Theory Day in Computer Science (DACS 2014)”, Analele Universitatii Bucuresti, Informatica, Anul LXI, pp 105–115
Cignoli R, Esteva F, Godo L, Torrens A (2000) Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Comput 4:106–112CrossRef
Di Nola A, Georgescu G, Iorgulescu A (2002a) Pseudo-BL algebras I. Mult-Valued Log 8:673–714
Di Nola A, Georgescu G, Iorgulescu A (2002b) Pseudo-BL algebras II. Mult-Valued Log 8:715–750
Dvurecenskij A (2007a) Agliano–Montagna type decomposition of linear pseudo-hoops and its applications. J Pure Appl Algebra 211:851–861
Dvurecenskij A (2007b) Every linear pseudo-BL algebra admits a state. Soft Comput 11:495–501
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Georgescu G, Leustean L, Preoteasa V (2005) Pseudo-hoops. J Mult-Valued Log Soft Comput 11:153–184MathSciNetMATH
Metadata
Title
The decomposition of linearly ordered pseudo-hoops
Author
Rodica Ceterchi
Publication date
20-08-2016
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 19/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-016-2304-x

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