"],"article":{"juan":"51","zhaiyao_cn":"在许多场合下，要把论域中的每一个对象或元素区分开来是没有必要的.用粒计算的观点来看，由小的部分可以组成较大的粒.而在不同粒度层次上，人们常常用层次结构的方法来观察或处理数据.由于不同尺度对数据有不同的分割，也就会得到不同层次的信息粒度.这些不同的信息粒度常常用不同的标记来标注.本文先介绍了多标记信息系统的概念，为了引入序关系而重新定义了保序的信息变换函数，并给出了多标记序信息系统的概念.在多标记序信息系统中，利用新的保序的信息变换函数，可以获得知识粒度的一个层次结构.在每一个层次中，利用优势关系可以定义优势类和劣势类，并定义了知识粒的下近似、上近似，进而定义了粗糙度、信息熵、粗糙熵等概念.在不同层次之间，分别讨论了下近似、上近似、粗糙度、信息熵和粗糙熵随着粒度粗细变化而变化的有关性质，在不同的标记粒度层次下探索的知识不确定性的变化规律. 

","endNoteUrl_en":"https://jns.nju.edu.cn/EN/article/getTxtFile.do?fileType=EndNote&id=517","reference":"[1] 李德毅，刘常昱，杜 鷁等．不确定性人工智能．软件学报，2004，15(11)：1583~1594．
[2] 王国胤，张清华．不同知识粒度下粗糙集的不确定性研究．计算机学报，2008，31(9)：1588~1598．
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","bibtexUrl_cn":"//www.sanmikaiseki.com/jns/CN/article/getTxtFile.do?fileType=BibTeX&id=517","abstractUrl_en":"https://jns.nju.edu.cn/EN/Y2015/V51/I2/377","qi":"2","id":517,"nian":2015,"bianHao":"201409051","zuoZheEn_L":"Gu Shenming*, Hu Chao, Wu Weizhi, Wang Xia","juanUrl_en":"https://jns.nju.edu.cn/EN/Y2015","shouCiFaBuRiQi":"2015-03-06","qiShiYe":"377","qiUrl_cn":"//www.sanmikaiseki.com/jns/CN/Y2015/V51/I2","lanMu_cn":"","pdfSize":"769309","zuoZhe_CN":"顾沈明 * , 胡 超, 吴伟志, 王 霞","risUrl_cn":"//www.sanmikaiseki.com/jns/CN/article/getTxtFile.do?fileType=Ris&id=517","title_cn":"多标记序信息系统的不确定性研究


","jieShuYe":"383","endNoteUrl_cn":"//www.sanmikaiseki.com/jns/CN/article/getTxtFile.do?fileType=EndNote&id=517","zhaiyao_en":"In many real-life applications, it is impossible or unnecessary to distinguish individual objects or elements in universe of discourses. With the view point of granular computing, the notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. There are different granules at different levels of scale in data sets having hierarchical structures. These different granulations often use different labels to mark. The purpose of this study is to analyze representations of granules and uncertainty measures in multi-label ordered information systems. The concept of multi-label information systems is first reviewed. The notion of granular information transformation functions between ordered sets is redefined in multi-label information systems. These functions are ordered preserving. Then, the concept of multi-label ordered information systems is introduced. By employing the new functions of granular information transformation, hierarchical structures of granules with different levels of granulations are derived in multi-label ordered information systems. At each level of granulations, dominance classes and dominated classes determined by dominance relations are also produced. Lower and upper approximations of any subset of the universe of discourse constructed by both dominance classes and dominated classes in multi-label ordered information systems are further explored, and their properties are examined. Finally, uncertainty measures such as roughness, information entropy and rough entropy of an object set at each level of granulations are also presented as usual way in multi-label ordered information systems. Monotonic properties of these uncertainty measures with different levels of granulations are analyzed.

","bibtexUrl_en":"https://jns.nju.edu.cn/EN/article/getTxtFile.do?fileType=BibTeX&id=517","abstractUrl_cn":"https://jns.nju.edu.cn/CN/Y2015/V51/I2/377","zuoZheCn_L":"顾沈明 * , 胡 超, 吴伟志, 王 霞","juanUrl_cn":"https://jns.nju.edu.cn/CN/Y2015","lanMu_en":"","qiUrl_en":"https://jns.nju.edu.cn/EN/Y2015/V51/I2","zuoZhe_EN":"Gu Shenming*, Hu Chao, Wu Weizhi, Wang Xia","risUrl_en":"https://jns.nju.edu.cn/EN/article/getTxtFile.do?fileType=Ris&id=517","title_en":"Uncertainty measures in multi-label ordered information systems


","hasPdf":"true"},"authorNotes_cn":["（浙江海洋学院数理与信息学院，舟山，316022）"]}">

多标记序信息系统的不确定性研究


顾沈明 * , 胡 超, 吴伟志, 王 霞

南京大学学报(自然科学版)››2015, Vol. 51››Issue (2): 377-383.

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南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (2) : 377-383.

多标记序信息系统的不确定性研究


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Uncertainty measures in multi-label ordered information systems


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{{article.zuoZheCn_L}}.{{article.title_cn}}[J]. {{journal.qiKanMingCheng_CN}}, 2015, 51(2): 377-383
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