On Implicative Derivations of MTL-Algebras

被引：0
|
作者：
Liu, Jianxin [1 ]
Li, Yijun [2 ]
Yang, Yongwei [3 ]
Wang, Juntao [4 ]
机构：
[1] Xinyang Normal Univ, Coll Teacher Educ, Xinyang 464000, Peoples R China
[2] Guangdong Univ Finance, Sch Financial Math & Stat, Guandzhou 510521, Peoples R China
[3] Anyang Normal Univ, Sch Math & Stat, Anyang 455000, Peoples R China
[4] Xian Shiyou Univ, Sch Sci, Xian 710065, Peoples R China
来源：
AXIOMS | 2022年 / 11卷 / 07期
基金：
中国国家自然科学基金;
关键词：
MTL-algebra; implicative derivation; k-modal operator; Galois connection; F-DERIVATIONS;
D O I：
10.3390/axioms11070340
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper introduces the implicative derivations and gives some of their characterizations on MTL-algebras. Furthermore, we provide some representation of MTL-algebras by implicative derivations and obtain some representation of Boolean algebra via the algebra of all implicative derivations. Finally, we explore the relationship between implicative derivation and other operators on MTL-algebras and show that there exists a bijection between the sets of multiplier and implicative derivations on IMTL-algebras. The results of this paper can provide the common properties of implicative derivations in the t-norm-based fuzzy logical algebras.
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页数：12
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