Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (9): 57-62.DOI: 10.3778/j.issn.1002-8331.1511-0253

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Annihilator operators and[⊕]ideals of IMTL-algebra with their relationships

WANG Lunlei, WU Hongbo   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Online:2017-05-01 Published:2017-05-15



  1. 陕西师范大学 数学与信息科学学院,西安 710062

Abstract: The main purpose is to study the properties of annihilator operator and[⊕]ideal with relationships among them. Firstly, the concept of annihilator operator is introduced into IMTL-algebras. The properties of single-point annihilator operator and multiple-point annihilator operator have been investigated respectively. Secondly, [⊕]ideal is introduced to IMTL-algebras and its some basic properties are discussed. Finally, the dependent relationship and decision relationship between annihilators and[⊕]ideals are explored.

Key words: fuzzy logic, logic algebra, IMTL-algebras, annihilator operator, [⊕]ideal

摘要: 主要对IMTL-代数中的零化算子和[⊕]理想的性质及其相互关系进行了研究。首先,将零化算子的概念引入到IMTL-代数中,在IMTL-代数中分别讨论了单点零化算子,多点零化算子的性质;其次,将[⊕]理想的概念引入IMTL-代数中,并对[⊕]理想的基本性质进行了讨论;最后,给出了IMTL-代数上零化子和[⊕]理想之间的相互依赖的关系和相互决定的方法。

关键词: 模糊逻辑, 逻辑代数, IMTL-代数, 零化算子, [&oplus, ]理想