On axiomatic characterizations of three pairs of covering based approximation operators.

*(English)*Zbl 1186.68470Summary: Rough set theory is a useful tool for dealing with inexact, uncertain or vague knowledge in information systems. The classical rough set theory is based on equivalence relations and has been extended to covering based generalized rough set theory. This paper investigates three types of covering generalized rough sets within an axiomatic approach. Concepts and basic properties of each type of covering based approximation operators are first reviewed. Axiomatic systems of the covering based approximation operators are then established. The independence of axiom set for characterizing each type of covering based approximation operators is also examined. As a result, two open problems about axiomatic characterizations of covering based approximation operators proposed by W. Zhu and F. Y. Wang in [IEEE Trans. Knowl. Data Eng. 19, No. 8, 1131–1144 (2007); Proceedings of the Third IEEE International Conference on Intelligent Systems, 2006, 444–449 (2006)] are solved.

##### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

##### Keywords:

axioms; covering based approximation operators; covering generalized rough sets; rough sets
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\textit{Y.-L. Zhang} et al., Inf. Sci. 180, No. 2, 274--287 (2010; Zbl 1186.68470)

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