摘要:通过语义分析，提出了一种拓展的粗糙集不确定性度量公理化定义；将香农熵函数推广到严凹函数，提出了一类以条件概率为自变量、基于严凹函数的粗糙集不确定性度量公式，它是严凹函数值的加权平均.在此基础上，得到一系列粗糙集不确定性度量方法.从严凹函数视角讨论了基于模糊熵的不确定性度量方法，发现现有多种能够用于度量粗糙集不确定性的模糊熵函数都是所提出方法的特殊情形.比较了粗糙度、改进粗糙度和所提出方法的区别和联系，最后设计了一些算例，比较了各种方法的异同，验证了基于严凹函数的粗糙集不确定性度量与粗糙集不确定性语义是一致的.



Abstract:Based on the semantic analysis, a general axiomatic definition of uncertainty measure for rough set is proposed. By extending the Shannon entropy function to strictly concave function, a class of uncertainty measures based on strictly concave function are put forward. They are weighted average of strictly concave function, whose variable is a conditional probability. It follows that a series of measuring methods are developed. The measuring methods based on fuzzy entropy are discussed under the view of strictly concave function. It is proved that they are the special cases of the method proposed in this paper. The difference and relationship among roughness measure, modified rough measure and the uncertainty measure based on strictly concave function are discussed. Finally, some examples are designed to compare the methods discussed in this paper. It is found that the proposed uncertainty measures based on strictly concave function are consistent with the semantics of uncertainty of rough set.



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