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Interval rough number covering rough set model. (Chinese. English summary) Zbl 1463.03030

Summary: At present, the existed covering rough sets only discussed the case where the elements in the domain are valued as real numbers, interval numbers or finite set-values. The discussion on the value of the interval rough numbers has not been seen. For this kind of situation, the covering rough set model based on interval rough numbers is proposed in this paper. Firstly, on the basis of the interval rough number the concept of the compatibility is defined by the parameters \(\alpha\) and \(\gamma\), and the definitions of the compatible relation and the compatible classes are further put forward. Then the concept of set dispersion is introduced to improve the upper and lower approximation which is defined by similar classes, and then the upper and lower approximation based on \(\xi\) set dispersion and the minimum set dispersion are proposed. It is proved that the fidelity of the model is increased. Finally, the accuracy of the minimum set dispersion based model is discussed.

MSC:

03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
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