计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (9): 45-49.

• 理论研究、研发设计 • 上一篇    下一篇

MV代数的子代数及相关重言式之间的关系

周建仁,吴洪博   

  1. 陕西师范大学 数学与信息科学学院,西安 710062
  • 出版日期:2013-05-01 发布日期:2016-03-28

Structure of subalgebra of MV-algebra with relations between tautologies on them

ZHOU Jianren, WU Hongbo   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Online:2013-05-01 Published:2016-03-28

摘要: 对MV单位区间[[0,1]]和n-值MV代数[Ln]的子代数的结构问题及其上重言式之间的关系进行了较为细致的研究。主要结论是:如果MV单位区间[[0,1]]的子代数[M]同构于n-值MV代数[Ln]的子代数,那么,存在正整数[m]满足[(m-1)|(n-1)]使得[M=Lm];如果[M]是MV单位区间[[0,1]]的子代数,那么或[M]为有限MV代数[Ln],或[M]为区间[[0,1]]上包含[{0,1}]的稠密集;若正整数[n-1]可分解为[(m1-1)(m2-1)?(mt-1)],其中[m1-1,m2-1,?,mt-1]是两两互素的正整数,则[Ln]是[Lm1,Lm2,?,Lmt]生成的MV代数;[T([0,1])=n=2∞T(Ln)],其中[T(M)]表示MV代数[M]上全体重言式之集合。

关键词: 模糊逻辑, Lucasiewicz逻辑系统, 多值逻辑代数(MV), 子代数, 重言式

Abstract: The structures of subalgebras of MV unit interval [[0,1]] and n-valued MV algebra [Ln] with  the relations of tautologies on them are studied intensively. The main results of this paper are as follows: if a subalgebra [M]of MV unit interval [[0,1]] is isomorphism to a subalgebra of MV algebra [Ln], then there exists a positive integer [m] such as [(m-1)|(n-1)] and [M=Lm]; if [M]is a subalgebra of MV unit interval [[0,1]], then [M] is an n-valued MV algebra [Ln], or [M]is a dense subset of [[0,1]] containing [{0,1}]; if positive integer [n-1] can be factored as [(m1-1)(m2-1)?(mt-1)] with positive integers [m1-1,m2-1,?,mt-1] relatively prime in pairs, then MV algebra [Ln] can be generated by subalgebras [Lm1,Lm2,?,Lmt]; [T([0,1])=n=2∞T(Ln)], where [T(M)] is the set of all tautologies on MV-algebra [M].

Key words: fuzzy logic, Lucasiewicz-logic system, algebras of Many-Valued logics(MV), subalgebra, tautology