New measures of uncertainty based on the granularity distribution of approximation sets

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Abstract

Uncertainty measures can help people to effectively analyze data and to reveal the essential characteristics of data sets. The roughness, accuracy and approximation accuracy are effective evaluations of uncertainty measure based on the lower and upper approximation sets in the classical rough set. However, due to the lack of consideration of the size of the granularity and the granulation distribution of approximation sets, the classical uncertainty measures and its improved methods still have suffered from some shortcomings, such as inaccurate measurement in some special cases, inconsistent with people’s cognition and so on, which motivate the study in this paper. In view of the fact that the upper and lower approximation sets are the basic concepts which are used to express the imprecision of knowledge. The paper introduces a more appropriate measure for evaluating the uncertainty, which combines the granularity of knowledge, the cardinality of the lower and upper approximation sets and the granularity distribution of the lower and upper approximation sets. Firstly, the roughness and accuracy based on the granularity distribution of the approximation sets are proposed, and the corresponding properties of the new roughness and accuracy are discussed. Two types of definitions of the approximation accuracy are investigated in the decision systems and their some properties are induced. Theoretical analyses indicate that the proposed measurements can be used to reasonably evaluate the uncertainty of information systems and decision systems. Finally, some experiments on nine UCI data sets are conducted and experimental results demonstrate that the proposed methods of uncertainty measurements are effective for evaluating the uncertainty of rough sets.

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