基于赋范格H 蕴涵代数的性质

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1465-1473.

基于赋范格H 蕴涵代数的性质

赖家俊^{1, 2}|徐扬¹|秦克云¹

1.西南交通大学智能控制开发中心成都 610031|2.西南交通大学信息科学与技术学院成都 610031

收稿日期:2007-06-25 修回日期:2009-12-10 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
国家自然科学基金(60474022, 60875034)和高等学校博士学科点专项科研基金(20060613007)资助

The Properties of Normed Lattice H Implication Algebras

LAI Jia-Jun^{1, 2}, XU Yang¹, QIN Ke-Yun¹

1.Intelligent Control Development Center, |Southwest Jiaotong University, Chengdu 610031;
2.School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031

Received:2007-06-25 Revised:2009-12-10 Online:2010-12-25 Published:2010-12-25
Supported by:
国家自然科学基金(60474022, 60875034)和高等学校博士学科点专项科研基金(20060613007)资助

摘要/Abstract

摘要：

首先, 在范数的条件下将格H 蕴涵代数进行了扩充(即赋范格H 蕴涵代数), 并讨论了它的性质. 其次, 在赋范格H 蕴涵代数中定义了蕴涵距离d_→, v -距离d_v, ∧-距离d_∧, 讨论了它们之间的性质, 并通过两个赋范格H 蕴涵代数L₁和L₂定义了赋范蕴涵满射、赋范格H 蕴涵同态、赋范格H 蕴涵同构以及赋范同构, 随后研究了它的性质.最后, 探讨了收敛数列的有界性, 得到了数列运算(即$\otimes$, $\oplus$, ∨, ∧, →)对于蕴涵距离是有界的结论.

关键词: 赋范格H 蕴涵代数, 蕴涵距离, 赋范蕴涵同态, 赋范同构, 有界性

Abstract:

Firstly, in this paper, under a norm situation, the notion of lattice H implication algebra L^[15]is extended (i.e., normed lattice H implication algebras), and some properties are discussed. Secondly, with the properties of implication distance d_→, v -distance d_v and ∧-distance d in normed lattice H implication algebras L investigated, the authors also define norned implication epimorphism、normed lattice H implication
homomorphism、normed lattice H implication isomorphism and normed isomorphism by using of a mapping f which has two normed lattice H implication algebras L₁ and L₂ together with its properties studied. Finally, the authors further probe into the boundedness
of convergence sequence, showing that sequences operations (i.e., $\otimes$, $\oplus$, ∨, ∧, →) to implication distance is bounded.

Key words: Normed lattice H implication algebra, Implication distance, Normed implication homomorphism, Normed isomorphism, Boundedness

中图分类号:

03B50

赖家俊, 徐扬, 秦克云. 基于赋范格H 蕴涵代数的性质[J]. 数学物理学报, 2010, 30(6): 1465-1473.

LAI Jia-Jun, XU Yang, QIN Ke-Yun. The Properties of Normed Lattice H Implication Algebras[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1465-1473.

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