The Model of Fuzzy Variable Precision Rough Sets

One limitation of the fuzzy rough sets is its sensitivity to the perturbation of original numerical data. In this paper we construct a model of fuzzy variable precision rough sets (FVPRS) by combining the fuzzy rough sets and variable precision rough sets, which is non-sensitive to the perturbation of the original numerical data. First, the fuzzy lower and upper approximations of FVPRS model are defined, and their properties are described. Second, the concepts of attributes reduction of FVPRS model, such as attributes reduct, core and positive region, etc, are defined. Third, a discernibility matrix is adopted to develop an algorithm to obtain all the attributes reduction of FVPRS. By the strict mathematical reasoning, we prove that the results obtained by the algorithm based on the discernibility matrix are the exact attributes reducts of FVPRS. Finally, the experimental results demonstrate that the model of FVPRS is feasible and effective in the real problems.