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] |
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| Database: | Engineering Source |
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