Abstract
The concept of (crisp) set is now extended to fuzzy set and rough set. The key notion of rough set is the two boundaries, the lower and upper approximations, and the lower approximation must be inside of the upper approximation. This inclusive condition makes the inference using rough sets complex: each approximation can not be determined independently. In this paper, the probabilistic inferences on rough sets based on two types of interpretation of If-Then rules, conditional probability and logical implication, are discussed. There are some interesting correlation between the lower and upper approximation after probabilistic inference.
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Yamauchi, Y., Mukaidono, M. (2001). Probabilistic Inference and Bayesian Theorem on Rough Sets. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_8
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DOI: https://doi.org/10.1007/3-540-45554-X_8
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