Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (8): 59-65.DOI: 10.3778/j.issn.1002-8331.1806-0340

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[(I,A)]-Implication and Its Basic Properties

LI Ying, ZHOU Hongjun   

  1. College of Mathmatics and Information Science, Shaanxi Normal University, Xi’an 710119, China
  • Online:2019-04-15 Published:2019-04-15


李  颖,周红军   

  1. 陕西师范大学 数学与信息科学学院,西安 710119

Abstract: Fuzzy implications play a fundamental role in fuzzy logic and approximate reasoning, and the construction of fuzzy implications is an important research topic in related fields. [(I,A)]-operators are constructed based on fuzzy implications [I] and aggregation operators [A]. The conditions under which [(I,A)]-operators are fuzzy implications are inverstigated, and the basic properties of [(I,A)]-implications are discussed, including distributivity over overlap functions and grouping functions and law of importation.

Key words: fuzzy implication;aggregation operator, [(I,A)]-implication;distributivity, law of importation

摘要: 模糊蕴涵在模糊逻辑和近似推理领域中发挥着十分重要的作用,模糊蕴涵的构造是相关领域中的重要研究课题。基于模糊蕴涵[I]和聚合算子[A]构造出[(I,A)]-算子,研究[(I,A)]-算子成为模糊蕴涵的条件,其次研究[(I,A)]-蕴涵包括分配性和输入性在内的一些基本性质。

关键词: 模糊蕴涵, 聚合算子, [(I, A)]-蕴涵, 分配性, 输入律