Dealing with uncertainty: A rough-set-based approach with the background of classical logic

Kádek, Tamás and Mihálydeák, Tamás (2021) Dealing with uncertainty: A rough-set-based approach with the background of classical logic. Annales Mathematicae et Informaticae, 53. pp. 157-168. ISSN 1787-6117

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Abstract

The representative-based approximation has been widely studied in rough set theory. Hence, rough set approximations can be defined by the system of representatives, which plays a crucial role in set approximation. In the authors’ previous research a possible use of the similarity-based rough set in first-order logic was investigated. Now our focus has changed to representative-based approximation systems. In this article, the authors show a logical system relying on representative-based set approximation. In our approach, a three-valued partial logic system is introduced. Based on the properties of the approximation space, our theorems prove that in some cases, there exists an efficient way to evaluate the first-order formulae.

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