摘要
针对现有粗糙集不确定性度量中有些定义在某种情况下并不合理,给出粗糙集不确定性度量的基本准则,证明除二次模糊度外其它几种不确定性度量都是满足基本准则的不确定性度量.由于满足基本准则的不确定性度量仍然可能存在不足,文中对基本准则中的单调性进行进一步限制,提出不确定性度量的扩展准则,并证明模糊熵和修正模糊度是满足扩展准则的不确定性度量,而粗糙度、粗糙熵和线性模糊度都不满足扩展准则.这些结论为已有的不确定性度量的合理性(或不合理性)提供理论说明,也为设计新的不确定性度量方法提供依据.
Since some uncertainty measures of rough sets are unreasonable under some circumstances, a basic rule set of uncertainty measure of rough set is proposed from the perspective of intuition. All the uncertainty measures except the quadratic fuzziness satisfy the basic rule set. The uncertainty measures satisfying the basic rule set still have unreasonability, and thus an extended rule set is further developed. The fuzzy entropy and revised fuzziness are the uncertainty measures satisfying the extended rule set, while the roughness, rough entropy and linear fuzziness are not. The results provide theoretical basis of the reasonability or unreasonability for the existing uncertainty measures, and it is a foundation for designing new uncertainty measures.
出处
《模式识别与人工智能》
EI
CSCD
北大核心
2010年第5期606-615,共10页
Pattern Recognition and Artificial Intelligence
基金
国家自然科学基金项目(No.60573068
60773113)
重庆市自然科学基金重点项目(No.2008BA2017)
重庆市杰出青年科学基金项目(No.2008BA2041)资助
关键词
不确定性
粗糙度
粗糙熵
模糊度
模糊熵
粗糙集
Uncertainty, Roughness, Rough Entropy, Fuzziness, Fuzzy Entropy, Rough Set
