集合概念的扩张与完善  

The Expanding and Perfect of Sets Conception

作　　者：王清印[1] 刘志勇[1] 

机构地区：[1]河北经贸大学不确定性系统研究所,河北石家庄050091

出　　处：《数学的实践与认识》2005年第7期224-231,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助课题(70271006);河北省社科规划项目(2002020006)

摘　　要：从集合概念的内涵出发,剖析了单值集——Cantor集合、Fuzzy集合、Rough集合、可拓集合概念的内涵;剖析了复值集——Grey集合、未确知集合、Vague集合、泛灰(UG)集合和广义泛灰(GUG)集合的内涵;从而得出广义泛灰集合是内涵最深的集合概念;它具有极强的描述能力,可以描述客观存在的一切现象,故又是外延最广的集合概念.From the meaning of sets, the paper analyses the meaning of the Single Value Sets,which includes Cantor Sets, Fuzzy Sets, Rough Sets and Extension Sets. It＇s also analyses the meaning of the Complex Value Sets, which includes Grey Sets, Unascertained Sets, Vague Sets. Universal Grey Sets and Generaliged Unlrersal Grey Sets. From which, it concludes that the Generaliged Universal Grey Sets is the deepest meaning of sets, and it has the stronger describing capability. It can describe all impersonality phenomenon, so it＇s the most extensive sets conception.

关 键 词：单值集 CANTOR集合 FUZZY集合 Rough集合 可拓集合 复值集 rey集合 未确知集合 Vague集合 泛灰集合 

分 类 号：O144[理学—数学]