计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (35): 90-92.

• 学术探讨 • 上一篇    下一篇

泛逻辑学中UB代数系统的滤子与商代数

肖云萍,邹庭荣   

  1. 华中农业大学 理学院 计算机系,武汉 430070
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-12-11 发布日期:2007-12-11
  • 通讯作者: 肖云萍

Filters and quotient algebra of UB algebras in universal logic

XIAO Yun-ping,ZOU Ting-rong   

  1. Dept. of Computer Science,College of Science and Technology,Huazhong Agricutural University,Wuhan 430070,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2007-12-11 Published:2007-12-11
  • Contact: XIAO Yun-ping

摘要: 给出了理想状态下泛逻辑学的形式演绎系统,证明了此系统是可靠的。提出了在理想状态(h=k=0.5)下泛逻辑学对应的代数系统-UB代数,进一步讨论了UB代数滤子与商代数,得到一些有用的结果。

关键词: 泛逻辑学, UB代数系统, 模糊逻辑, 滤子, 商代数

Abstract: Introduce the concept of filter and quotient algebra of UB algebras,further basic properties are investigaled:Theorem A nonempty set F of M be a filter if and only if xyyzF,则xzF;and F be a implicative filter of M;if and only if F be filter and y→(yx)∈F implies yxF;if and only if F be filter and z→(y→(yx))∈FzF implies yxF;if and only if z→(yx)∈M implies(zy)→(zx)∈F;if and only if zF and z→((xy)→x)∈F implies xF;if and only if F be filter and (xy)→xF implies xF;etc.

Key words: universal logic, UB-algebras, fuzzy logic, filter, quotient algebra