Abstract
We review concepts and principles of Modus Ponens and Modus Tollens in the areas of rough set theory and probabilistic inference. Based on the upper and the lower approximation of a set as well as the existing probabilistic results, we establish a generalized version of rough Modus Ponens and rough Modus Tollens with a new fact different from the premise (or the conclusion) of “if ...then ...” rule, and address the problem of computing the conditional probability of the conclusion given the new fact (or of the premise given the new fact) from the probability of the new fact and the certainty factor of the rule. The solutions come down to the corresponding interval for the conditional probabilities, which are more appropriate than the exact values in the environment full of uncertainty due to errors and inconsistency existed in measurement, judgement, management, etc., plus illustration analysis.
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Acknowledgments
The authors would like to thank the reviewers for their comments that help improve the manuscript. This research was supported in parts by the National Natural Science Foundation of China (No. 61273304, 61202170, 61573255, 61573259), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130072130004), and the program of Further Accelerating the Development of Chinese Medicine Three Year Action of Shanghai (2014–2016) (No. ZY3-CCCX-3-6002).
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Yao, N., Miao, D., Zhang, Z., Lang, G. (2016). Probabilistic Estimation for Generalized Rough Modus Ponens and Rough Modus Tollens. In: Flores, V., et al. Rough Sets. IJCRS 2016. Lecture Notes in Computer Science(), vol 9920. Springer, Cham. https://doi.org/10.1007/978-3-319-47160-0_15
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DOI: https://doi.org/10.1007/978-3-319-47160-0_15
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