Novel probabilistic approach to generating rough sets

Raisa R. Szabo

doi:10.1117/12.304851

25 March 1998 Novel probabilistic approach to generating rough sets

Raisa R. Szabo

Proceedings Volume 3390, Applications and Science of Computational Intelligence; (1998) https://doi.org/10.1117/12.304851
Event: Aerospace/Defense Sensing and Controls, 1998, Orlando, FL, United States

Abstract

Rough set theory, introduced by Pawlak in the early 1980s, in a mathematical tool to deal with vagueness and uncertainty. In contract, for centuries, uncertainty was measured in terms of probability theory. In this paper a novel method based on the Bayesian approach is proposed to generate the rough set decisions. The results of this approach may be summarized as the following: (1) The classification accuracy of a concept can be calculated as a prior probability of the class. (2) The accuracy of approximation of each atomic event equals the posterior probability of the atomic event. The posterior probability can be calculated using the lower and the upper approximations of the event. These accuracy measures can then be used to derive the final decision. (3) Normalized class conditional probabilities can be used to determine the significance of attributes. In addition, a minimal (reduced) subset, which ensures a satisfactory quality of approximation, can be calculated as a product of the accuracy of approximation of each event and the frequency of the event in the original set. The reduced set, however, does not play any role in the decision making process if the proposed probabilistic approach is utilized.

Citation Download Citation

Raisa R. Szabo "Novel probabilistic approach to generating rough sets", Proc. SPIE 3390, Applications and Science of Computational Intelligence, (25 March 1998); https://doi.org/10.1117/12.304851

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