R0-similarity relation between fuzzy sets and its properties

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (31): 53-56.

• 研究、探讨 • Previous Articles Next Articles

R₀-similarity relation between fuzzy sets and its properties

LIU Jie，WU Hongbo

College of Mathematics and Information Sciences，Shaanxi Normal University，Xi’an 710062，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-11-01 Published:2011-11-01

模糊集间的R₀-相似关系及其性质

刘杰，吴洪博

陕西师范大学数学与信息科学学院，西安 710062

Abstract

Abstract: 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 R₀implication，and its properties are discussed in detail.Finally，several examples of [R0]-similarity relation are provided by the R₀implication 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.

Key words: fuzzy mathematics, fuzzy logic, R₀-type logic system, R₀-implication operator, R₀-similarity relation

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。

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

LIU Jie，WU Hongbo. R₀-similarity relation between fuzzy sets and its properties[J]. Computer Engineering and Applications, 2011, 47(31): 53-56.

刘杰，吴洪博. 模糊集间的R₀-相似关系及其性质[J]. 计算机工程与应用, 2011, 47(31): 53-56.

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R₀-similarity relation between fuzzy sets and its properties

模糊集间的R₀-相似关系及其性质

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