Monotonic Uncertainty Measures in Probabilistic Rough Set Model
Uncertainty measure is one of the key research issues in the rough set theory. In the Pawlak rough set model, the accuracy measure, the roughness measure and the approximation accuracy measure are used as uncertainty measures. Monotonicity is a basic property of these measures. However, the monotonicity of these measures does not hold in the probabilistic rough set model, which makes them not so reasonable to evaluate the uncertainty. The main objective of this paper is to address the uncertainty measure problem in the probabilistic rough set model. We propose three monotonic uncertainty measures which are called the probabilistic accuracy measure, the probabilistic roughness measure and the probabilistic approximation accuracy measure respectively. The monotonicity of the proposed uncertainty measures is proved to be held. Finally, an example is used to verify the validity of the proposed uncertainty measures.
KeywordsUncertainty measures approximation accuracy Pawlak rough set model probabilistic rough set model
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