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中文摘要：
首先，在给出了反例证实现有方法在某些情况得出的结果与实际结论不一致情况下，提出了一个真正考虑了两种因素的改进的vague集模糊熵公理化定义；然后给出一种vague集模糊熵的新计算公式；最后通过定理证明和实例分析，指出它确实同时考虑到vague集的未知性和不确定性，从而证明所给出vague集模糊熵的定义是更加合理的。
英文摘要：
At first, this paper gave a counterexample to show that the result used the presented method in some cases and real conclusions were contrary, then proposed an improved axiom definition of the fuzzy entropy of vague sets that taking really into account two factors, and proposed a corresponding new formula of the fuzzy entropy of vague sets. Finally it pointed really tak- ing into account simultaneously the unknown and the uncertainty out by proved theorem and analyzed example. Then it proved that the definition of the fuzzy entropy of vague sets is more efficient and rational.
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The further investigation of covering-based rough sets: Uncertainty characterization, similarity mea
Global existence and uniqueness of solutions for fuzzy differential equations under dissipative-type
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