Characterizations of hoops based on stabilizers

In this paper, we characterize the algebraic structure of hoops via stabilizers. First, we further study left and right stabilizers in hoops and discuss the relationship between them. Then, we characterize some special classes of hoops, for example, Wajsberg hoops, local hoops, Gödel hoops and stabi...

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Bibliographic Details
Published inJournal of intelligent & fuzzy systems Vol. 39; no. 3; pp. 4341 - 4348
Main Authors Wang, Jun Tao, Borzooei, R. A., Aaly Kologani, M.
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2020
Subjects
Algebra
Fuzzy logic
Fuzzy systems
Hoops
Norms
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Summary:In this paper, we characterize the algebraic structure of hoops via stabilizers. First, we further study left and right stabilizers in hoops and discuss the relationship between them. Then, we characterize some special classes of hoops, for example, Wajsberg hoops, local hoops, Gödel hoops and stabilizer hoops, in terms of stabilizers. Finally, we further determine the relationship between stabilizers and filters in hoops and obtain some improvement results. This results also give answer to open problem, which was proposed in [Stabilizers in MTL-algebras, Journal of Intelligent and Fuzzy Systems, 35 (2018) 717-727]. These results will provide a more general algebraic foundation for consequence connectives in fuzzy logic based on continuous t-norms.
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-200345