Triangular Norms on Partially Ordered Sets.
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| Title: | Triangular Norms on Partially Ordered Sets. |
|---|---|
| Authors: | Su, Yong1 (AUTHOR) yongsu88@163.com, Tian, Feng1 (AUTHOR), Zong, Wenwen2 (AUTHOR), Mesiar, Radko3,4 (AUTHOR) |
| Source: | Mathematical Logic Quarterly. May2026, Vol. 72 Issue 2, p1-9. 9p. |
| Subjects: | Triangular norms, Partially ordered sets, Ordered algebraic structures, Homomorphisms, Semigroups (Algebra), Monotonic functions |
| Abstract: | In this study, we extend the additively generated triangular norms from the framework of the unit interval to that of partially ordered sets. We present several conditions under which this formula ψT(φx,φy)$\psi T(\varphi x, \varphi y)$ yields a t‐norm, where P,Q$P, Q$ are partially ordered sets, φ:P→Q$\varphi: P \rightarrow Q$ and ψ:Q→P$\psi: Q \rightarrow P$ are monotone functions and T$T$ is a t‐norm/t‐conorm on Q$Q$. The partially ordered semigroups induced by ψT(φx,φy)$\psi T(\varphi x, \varphi y)$ are order‐preserving/order‐reversing homomorphic to semigroup deformations of the semigroup induced by T$T$. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Logic Quarterly is the property of Wiley-Blackwell 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194135663 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Triangular Norms on Partially Ordered Sets. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Su%2C+Yong%22">Su, Yong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yongsu88@163.com</i><br /><searchLink fieldCode="AR" term="%22Tian%2C+Feng%22">Tian, Feng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zong%2C+Wenwen%22">Zong, Wenwen</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mesiar%2C+Radko%22">Mesiar, Radko</searchLink><relatesTo>3,4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Logic+Quarterly%22">Mathematical Logic Quarterly</searchLink>. May2026, Vol. 72 Issue 2, p1-9. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Triangular+norms%22">Triangular norms</searchLink><br /><searchLink fieldCode="DE" term="%22Partially+ordered+sets%22">Partially ordered sets</searchLink><br /><searchLink fieldCode="DE" term="%22Ordered+algebraic+structures%22">Ordered algebraic structures</searchLink><br /><searchLink fieldCode="DE" term="%22Homomorphisms%22">Homomorphisms</searchLink><br /><searchLink fieldCode="DE" term="%22Semigroups+%28Algebra%29%22">Semigroups (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Monotonic+functions%22">Monotonic functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this study, we extend the additively generated triangular norms from the framework of the unit interval to that of partially ordered sets. We present several conditions under which this formula ψT(φx,φy)$\psi T(\varphi x, \varphi y)$ yields a t‐norm, where P,Q$P, Q$ are partially ordered sets, φ:P→Q$\varphi: P \rightarrow Q$ and ψ:Q→P$\psi: Q \rightarrow P$ are monotone functions and T$T$ is a t‐norm/t‐conorm on Q$Q$. The partially ordered semigroups induced by ψT(φx,φy)$\psi T(\varphi x, \varphi y)$ are order‐preserving/order‐reversing homomorphic to semigroup deformations of the semigroup induced by T$T$. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Logic Quarterly is the property of Wiley-Blackwell 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/malq.70014 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 1 Subjects: – SubjectFull: Triangular norms Type: general – SubjectFull: Partially ordered sets Type: general – SubjectFull: Ordered algebraic structures Type: general – SubjectFull: Homomorphisms Type: general – SubjectFull: Semigroups (Algebra) Type: general – SubjectFull: Monotonic functions Type: general Titles: – TitleFull: Triangular Norms on Partially Ordered Sets. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Su, Yong – PersonEntity: Name: NameFull: Tian, Feng – PersonEntity: Name: NameFull: Zong, Wenwen – PersonEntity: Name: NameFull: Mesiar, Radko IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09425616 Numbering: – Type: volume Value: 72 – Type: issue Value: 2 Titles: – TitleFull: Mathematical Logic Quarterly Type: main |
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