Determination of the threshold value β of variable precision rough set by fuzzy algorithms

In the past, the choices of β values to be applied to find the β-reducts in VPRS for an information system are somewhat arbitrary. In this study, a systematic method which bridges the fuzzy set methodology and probabilistic approach of RS to solve the threshold value β determination problem in variable precision rough sets (VPRS) is proposed. Different from the existing probabilistic methods, the proposed method relies on the fuzzy membership degrees of each attribute of the objects to calculate β. The proposed method gives the membership degrees and fuzzy aggregation operators the probabilistic interpretations. Based on the probabilistic interpretations, the threshold value β of VPRS is directly derived from fuzzy membership degree by Implication Relations and Fuzzy Algorithms, in which the membership degrees are obtained by the standard Fuzzy C-means method. The argument is that errors of system classification would occur in the fuzzy-clustering phase prior to information classification, therefore the threshold value β should be constrained by the probability of belongingness of an object to the fuzzy clusters, i.e., through the values of membership functions. A few examples are given in the paper to demonstrate the differences with other β-determining methods.

► A method bridges fuzzy set and probabilistic approach of RS to solve the β value determination problem in VPRS is proposed.
► The proposed method gives the membership degrees and fuzzy aggregation operators the probabilistic interpretations.
► Errors of system classification occur in the fuzzy-clustering phase prior to information classification is considered.
► The threshold value β is constrained by the probability of belongingness through the values of membership functions.
► A few examples are given in the paper to demonstrate the differences with other β-determining methods.