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复合模糊命题运算中的弱范数研究
引用本文:安世虎.复合模糊命题运算中的弱范数研究[J].计算机学报,2001,24(10):1071-1076.
作者姓名:安世虎
作者单位:山东财政学院计算机信息工程系
摘    要:在模糊诊断和分析问题中,一个复合命题往往由多个子命题组成,子命题之间除有合取、析取及加权平均运算关系外,还存在一种非常重要的弱逻辑关系。对基于单一数值表达的模糊命题间的合取、析取关系的最一般运算形式是三角范数和三角余范数。该文给出基于单一数值表示模糊命题的弱逻辑关系的最一般运算形式f范数和基于区间值表示的模糊命题弱逻辑关系最一般运算形式f-范数,具体给出相关算子,讨论了它们的性质及与传统的一些算子之间的联系,通过引入强f范的概念,给出了构造f-范数算子的一般方法,对具有弱逻辑关系复合模糊命题的真值运算可采用本文介绍的概念和方法。

关 键 词:f范数  强f范数  弱逻辑关系  复合模糊命题运算  弱范数  专家系统
修稿时间:2000年6月7日

On the Weak Norms of the Compound Fuzzy Proposition
AN Shi-Hu.On the Weak Norms of the Compound Fuzzy Proposition[J].Chinese Journal of Computers,2001,24(10):1071-1076.
Authors:AN Shi-Hu
Abstract:During the course of fuzzy diagnosis and analysis, a compound fuzzy proposition often consists of many atomic propositions, in which there is still a very important weak logic besides conjunction,disjunction and weighted average operator. Triangular norms are a common form of conjunction operator to a real number based representation of the true value of a compound fuzzy proposition. Triangular conorms are also a common form of disjunction operator to a real number based representation of the true value to the compound fuzzy proposition. f norms are presented in the paper as a common form of weak logic operator to a real number based representation of the true value to the compound fuzzy proposition. f-norms are also presented in the paper for a common form of weak logic operator to an interval based representation of the true value to the compound fuzzy proposition. Some operators associated with weak norms are given in the paper. Characteristics and relationships of the operators are discussed.A common approach to creating f-norms is introduced by the concept of strong f norms. The concepts and methods in the article may be adapted in operating true value of weak logic compound fuzzy propositions.
Keywords:f norms    strong f norms    f-norms    weak  logic
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