摘要
Liu在文献[6]指出一个模糊集的模糊熵可由它与它的补集的相似度量来刻画.与模糊集不同的是,Vague集同时提供支持与反对的证据,因而它的模糊熵来自两方面,即未知信息和不确定性信息,首先在暂不考虑未知信息的前提下,将Liu的方法推广到Vague集上,然后以此为基础,给出一种同时考虑到上述两种影响因素的非概率型Vague熵公理准则及其计算公式,最后将它和现有的其它几种Vague熵计算公式进行比较,结果发现它与Szmidt等(2001)建议的公式完全等效,但它形式更简单、可操作性更强,并且它是Liu的方法在Vague集上的推广,这进一步揭示了Vague集和模糊集之间的内在联系.
It was pointed out by Liu in[6], that the fuzziness of a fuzzy set can be described by the similarity degree between the tuzzy set and its complement. But vague set is very different from fuzzy set because it presents favoring and opposing evidence simultaneously. The fuzziness of vague sets mainly comes from unknown and uncertainty information. At first, without unknown information, Liu＇s method is extended to vague sets in this paper. Then an axiomatized non-probabilistic vague entropy, which takes into account two factors above simultaneously, is proposed and a corresponding formula is presented. Finally, compared with other formulas, it is found that it can get the same result with the formula proposed by Szmidt and Kacprzyk. But it is simpler and more maneuverable and the inherent relations between fuzzy set and vague set are disclosed by the extension to vague set.
出处
《小型微型计算机系统》
CSCD
北大核心
2006年第11期2115-2119,共5页
Journal of Chinese Computer Systems
基金
广东省自然科学基金项目(034071)资助.
关键词
VAGUE集
相似度量
未知信息
不确定性信息
熵
vague set
similarity measure
unknown information
uncertainty information
entropy
