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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 75-82.doi: 10.6040/j.issn.1671-9352.0.2014.342

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MTL代数的Wajsberg形式及其应用

寇海燕, 吴洪博   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2014-07-25 修回日期:2014-11-20 出版日期:2015-02-20 发布日期:2015-01-27
  • 通讯作者: 吴洪博(1959-),男,博士,教授,研究方向为格上拓扑与非经典数理逻辑. E-mail:wuhb@snnu.edu.cn E-mail:wuhb@snnu.edu.cn
  • 作者简介:寇海燕(1989-),女,硕士研究生,研究方向为格上拓扑与非经典数理逻辑. E-mail:461316377@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11171196)

Wajsberg's form of MTL algebras with applications

KOU Hai-yan, WU Hong-bo   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-07-25 Revised:2014-11-20 Online:2015-02-20 Published:2015-01-27

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摘要： MTL代数是一种重要的基础逻辑代数.本文采用Wajsberg方法,根据逻辑系统MTL中公理的形式,建立了NMTL代数的经典代数表示形式,进而证明了NMTL代数与MTL代数是同一代数结构,证明了满足条件 ∀x,y∈L, x→y=(y→0)→(x→0)的NMTL代数L是BR0代数.在此基础上证明了IMTL代数和BR0代数是同一代数结构,并给出BR0代数和BL代数的Wajsberg形式.

关键词: NMTL代数, MTL代数, BL代数, 剩余格, BR0代数, 模糊逻辑

Abstract: MTL algebra is an important basic logic algebra. Firstly, the classical algebras forms of NMTL algebra is given by taking Wajsberg's method and some parts of axioms of MTL logic system, and it is proved that NMTL algebra and MTL algebra have identical structure. Secondly, it is proved that an NMTL algebras L satisfying the condition: ∀x,y∈L, x→y=(y→0)→(x→0) is BR0 algebra. Finally, it is proved that IMTL algebra and BR0 algebra have identical structure and the Wajsberg forms of BR0 algebra and BL algebra are given.

Key words: fuzzy logic, residuated lattice, NMTL algebra, BR0 algebra, BL algebra, MTL algebra

中图分类号: 

  • O141.1
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