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Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets

机译:广义模糊粗糙集不确定性的信息理论测度

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Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications. This paper studies the measurement of uncertainty in generalized fuzzy rough sets determined by a triangular norm. Based on information theory, the entropy of a generalized fuzzy approximation space is introduced, which is similar to Shannon's entropy. To measure uncertainty in generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T = min, it is proved that the measure of fuzziness of a generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable.
机译:粗糙集理论已被广泛确立为在各种应用中进行不确定性管理的机制。本文研究了由三角模确定的广义模糊粗糙集的不确定性度量。基于信息论,引入了广义模糊近似空间的熵,它与香农的熵相似。为了测量广义模糊粗糙集的不确定性,引入了模糊性的概念。研究了该措施的一些基本特性。对于一个特殊的三角形范数T = min,证明了当且仅当该集合是清晰且可定义的时,广义模糊粗糙集的模糊性度量才等于零。

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