Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
