模糊集间的R_0-相似关系及其性质  

R_0-similarity relation between fuzzy sets and its properties

作　　者：刘杰[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：《计算机工程与应用》2011年第31期53-56,62,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.10871121)~~

摘　　要：将王国俊教授在R0-型逻辑系统中建立的R0-蕴涵算子应用于模糊数学理论之中,在非空集合X为论域的模糊集族F(X)上定义了一种新型运算-R0蕴含运算,并讨论了F(X)上R0-蕴含运算的一些基本性质。通过R0-蕴含运算在F(X)上定义了一个二元模糊相似关系-R0-相似关系,并对其性质进行了较为详细的讨论。在有限论域X确定的模糊集族F(X)上给出了几个R0-相似关系的具体实例。R0-implication operator proposed by Professor Wang Guojun in the R0-type logic system has been applied to the fuzzy mathematical theory,and a new kind of computation-R0-implication operation,is defined on the family F（X） of fuzzy sets,and its basic properties have been discussed.Then,a binary fuzzy similarity relation-R0-similarity relation on F（X） is defined through the R0 implication,and its properties are discussed in detail.Finally,several examples of R0-similarity relation are provided by the R0 implication operator on F（X） with the finite domain X.Not only the results of this paper make an application of the R0-type logic system,but also enrich the methods of studying fuzzy mathematics.

关 键 词：模糊数学 模糊逻辑 R0-蕴涵算子 R0-型逻辑系统 R0-相似关系 

分 类 号：O159[理学—数学] O142[理学—基础数学]