R_O-蕴涵算子所导出的逻辑函数的特征  

The Characteristics of Logic Functions Determined by R_0-Implication Operator

作　　者：周建仁[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《数学学报（中文版）》2014年第2期235-248,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11171196);西安市科技计划项目(CX12189WL26)

摘　　要：R_0-蕴涵算子是王国俊在2000年建立的一种新型蕴涵算子.目前,R_0-蕴涵算子在模糊控制、近似推理、模糊识别、模糊系统、计量逻辑的研究方面有着重要应用,而这些应用的共同点,是公式通过R_0-蕴涵算子所导出的逻辑函数在其中发挥着关键的作用.本文在R_0-型命题逻辑系统中,对由n个原子公式生成的公式通过R_0-蕴涵算子导出的逻辑函数的特征进行了研究,得到了函数可由R_0-型命题逻辑系统中的公式通过R_0-蕴涵算子导出的充要条件.The R0-implication operator is a new implication operator that was pro- posed by Wang Guojun in 2000. In the present, the R0-implication operator has been applied to studying of fuzzy controlling, approximate reasoning, fuzzy recogni tion, fuzzy systems, quantitative logic. The common point of applications is that the function determined by a formula through R0-implication operator plays a key role. In this paper, the characteristics of the function determined by a formula through R0- implication operator are investigated intensively in Ro-style propositional logic system. The necessary and sufficient conditions are obtained for a function f ： [0, 1]n → [0, 1] to be induced by a formula through the R0-implication operator in R0-style propositional logic system.

关 键 词：模糊逻辑 R0-蕴涵算子 逻辑函数 

分 类 号：O141.1[理学—数学]