| 集合概念的扩张与完善 |
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| 引用本文： | 王清印,刘志勇.集合概念的扩张与完善[J].数学的实践与认识,2005,35(7):224-231. |
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| 作者姓名： | 王清印 刘志勇 |
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| 作者单位： | 河北经贸大学不确定性系统研究所,河北,石家庄,050091 |
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| 基金项目： | 国家自然科学基金资助课题(70271006)，河北省社科规划项目(2002020006) |
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| 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.
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| 关 键 词： | Cantor集合 Fuzzy集合 Rough集合 可拓集合 Grey集合 未确知集合 Vague集合 泛灰集合 广义泛灰集合 |
| 修稿时间： | 2004年12月10 |
The Expanding and Perfect of Sets Conception |
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| WANG Qing-yin,LIU Zhi-yong.The Expanding and Perfect of Sets Conception[J].Mathematics in Practice and Theory,2005,35(7):224-231. |
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| Authors: | WANG Qing-yin LIU Zhi-yong |
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| Abstract: | 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 Unirersal 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. |
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| Keywords: | cantor sets fuzzy sets rough sets extension sets grey sets unascertained sets vague sets universal grey sets generaliged universal grey sets |
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