中文核心期刊
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重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 1992, Vol. 11 ›› Issue (2): 1-7.

• •    下一篇

关于一类α-值和连续值逻辑函数的组合网络实现问题

李俊雄   

  1. 重庆交通学院管理工程系
  • 收稿日期:1991-05-14 出版日期:1992-04-20 发布日期:2016-11-08
  • 作者简介:李俊雄,男,28岁,助教,本文受院青年基金资助

Some Results on the Finite Complete Set of the Multi Valued Logic and Fuzzy Logic Functions

Li Junxiong   

  1. Management Engineering Department
  • Received:1991-05-14 Online:1992-04-20 Published:2016-11-08

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摘要： 对于某类函数的集合A,如果存在一个有限集C⊆A,使得A中的任意函数均可以由C的一个有限组合函数网络实现,则称C是A的一个有限完备集。如,函数集{x∧x,x∨x,x}是二值逻辑函数的有限完备集。本文给出一个4个函数组成的集合,并证明这个集合是一类多值逻辑函数的有限完备集。本文还证明,对于模糊逻辑函数,不存在有限完备集。此外,本文建立了形式演算系统FUNCc,并证明C上的一个组合函数网络与FUNCTc的一个定理等价。

关键词: 组合函数网络, 完备集, 多值逻辑, 模糊逻辑, 形式演算

Abstract: Given any set A whoso elements are functions,if there exists a finite set C,C≡A,such that each function in set A can be implemented by a combinatorial network of the functions in set C,it is said that C is a finite complete set of the functions in A.For example,the function set (x∧x,x∨x,x) is just a finite complete set of the two-valued logic functions.In this paper,a set consisting of 4 functions is given and proved to be a finite complete.set of the α-valued logic functions (α≥2).It is aiso proved that no finite complete set exists for the fuzzy logic functions.In addition to the above results,a formal inference system FUNCc is created and it is proved that each combinatorial network of the functions in C is equivalent to a theorem of the FUNCc.

Key words: combinatorial network of functions, complete set, multi-valued logic, fuzzy logic, formal inference