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剩余格与正则剩余格的特征定理
引用本文:裴道武.剩余格与正则剩余格的特征定理[J].数学学报,2002,45(2):271-278.
作者姓名:裴道武
作者单位:西安交通大学理学院,陕西,西安,710049;盐城师范学院数学系,江苏,盐城,224002
摘    要:本文进一步研究了具有广泛应用的一类模糊逻辑代数系统——剩余格,并引入了正则剩余格的概念,对剩余格与正则剩余格的定义进行了讨论,给出了剩余格与正则剩余格的特征定理,其中包含剩余格与正则剩余格的等式特征,从而这两个格类都构成簇.本文还讨论了剩余格与正则剩余格公理系统的独立性,以及它们与相近代数结构的关系.

关 键 词:模糊逻辑  代数系统  剩余格  正则剩余格  特征
文章编号:0583-1431(2002)02-0271-08
修稿时间:2000年5月17日

The Characterization of Residuated Lattices and Regular Residuated Lattices
PEI Dao Wu.The Characterization of Residuated Lattices and Regular Residuated Lattices[J].Acta Mathematica Sinica,2002,45(2):271-278.
Authors:PEI Dao Wu
Institution:PEI Dao Wu (Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China) (Department of Mathematics, Yancheng Teachers College, Yancheng 224002, P. R. China)
Abstract:In this paper, the residuated lattices are further studied because of their wide applications, and a kind of new fuzzy logic algebra structure-regular residuated lattices are introduced. The concepts and properties of residuated lattices and regular residuated lattices are discussed, and some characteristic theorems are obtained. In them, there are the equational characterization of residuated lattices and regular residuated lattices. This shows that the classes of all residuated lattices and all regular residuated lattices form varieties. In this paper, the independence problem of axiom systems of residuated lattices and regular residuated lattices also are studied.
Keywords:Fuzzy logic  Algebra system  Residuated lattice  Regular residuated lattice  Characterization
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