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ET-norms and n-roots on EBL-algebras.

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Title: ET-norms and n-roots on EBL-algebras.
Authors: Tao Liu1 2071341378@qq.com, Hongxing Liu2 lhxshanda@163.com
Source: IAENG International Journal of Applied Mathematics. May2025, Vol. 55 Issue 5, p1227-1234. 8p.
Subjects: Square root
Abstract: In this paper, we will define the notion of Etnorms (Et-conorms) as an extension of t-norms (t-conorms). We also introduce some important properties of Et-norms (Etconorms) on an chain. For example, we characterize strictly monotonicity and continuity of Et-norms (Et-conorms) on an chain. In addition, we introduce some important results between an Et-norm T on an chain L and an EBL-algebra (L, ∨, ∧, T, 0). On the other hand, we give the notion of nroots on EBL-algebras and study their main properties. In addition, we define the notion for an EBL-homomorphism to preserve n-roots and prove a necessary and sufficient condition for an EBL-homomorphism to preserve n-roots. Finally, we introduce the notion of strict n-roots and characterize some properties of n-strict EBL-algebras. Particularly, we prove each n-strict EBL-algebra is a BL-algebra. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: ET-norms and n-roots on EBL-algebras.
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  Data: <searchLink fieldCode="AR" term="%22Tao+Liu%22">Tao Liu</searchLink><relatesTo>1</relatesTo><i> 2071341378@qq.com</i><br /><searchLink fieldCode="AR" term="%22Hongxing+Liu%22">Hongxing Liu</searchLink><relatesTo>2</relatesTo><i> lhxshanda@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. May2025, Vol. 55 Issue 5, p1227-1234. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Square+root%22">Square root</searchLink>
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  Label: Abstract
  Group: Ab
  Data: In this paper, we will define the notion of Etnorms (Et-conorms) as an extension of t-norms (t-conorms). We also introduce some important properties of Et-norms (Etconorms) on an chain. For example, we characterize strictly monotonicity and continuity of Et-norms (Et-conorms) on an chain. In addition, we introduce some important results between an Et-norm T on an chain L and an EBL-algebra (L, ∨, ∧, T, 0). On the other hand, we give the notion of nroots on EBL-algebras and study their main properties. In addition, we define the notion for an EBL-homomorphism to preserve n-roots and prove a necessary and sufficient condition for an EBL-homomorphism to preserve n-roots. Finally, we introduce the notion of strict n-roots and characterize some properties of n-strict EBL-algebras. Particularly, we prove each n-strict EBL-algebra is a BL-algebra. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 8
        StartPage: 1227
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      – SubjectFull: Square root
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      – TitleFull: ET-norms and n-roots on EBL-algebras.
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            NameFull: Tao Liu
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            NameFull: Hongxing Liu
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            – D: 01
              M: 05
              Text: May2025
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              Y: 2025
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