Variable Precision Fuzzy Rough Set Model with Linguistic Labels

This paper presents an approach which combines unified variable precision fuzzy rough set model together with the concept of fuzzy linguistic labels. A real world application of the standard fuzzy rough sets can be problematic, especially in the case of large universes and noisy data. Due to relaxation of strict inclusion requirement in determining approximations of sets, a more tolerant variable precision fuzzy rough set model is better suited to be useful in analysis of this kind of data. Furthermore, a crucial issue at the initial stage of the fuzzy rough set approach consists in generating a fuzzy partition of a universe, with respect to condition and decision attributes. It requires comparing of elements by using a suitable fuzzy similarity relation. We simplify this process by applying the concept of fuzzy linguistic labels for determining the family of fuzzy similarity classes. This is done by performing a comparison of elements of the universe to a subset of representative elements which are described with the help of dominating linguistic values of attributes. The notions of the variable precision fuzzy rough set model, which is expressed in a unified parameterized form, can be used to determine the quality of the considered information system by evaluating its consistency, and to obtain a system of fuzzy decision rules.