An Approach to Parameterized Approximation of Crisp and Fuzzy Sets

This paper proposes a concept of parameterized approximation of crisp and fuzzy sets, basing on the notion of rough and fuzzy rough inclusion function. A definition of a single e-approximation is given. It is suitable for expressing the lower and upper approximations defined in the rough set theory and the variable precision rough set model. A unified form of approximation is especially advantageous in the case of fuzzy information systems. It helps to avoid problems caused by different forms of fuzzy connectives used in the original definition of fuzzy rough sets. The presented parameterized approach to approximation constitutes an easy to implement, straightforward generalization of the variable precision crisp and fuzzy rough set model.

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