Fuzzy neighborhood based variable-precision granular-ball rough sets with applications to feature selection

Granular-ball computing is an efficient, simple and scalable computing paradigm that has emerged in recent years. By sampling the data with multiple divisions, the knowledge on different granularity levels is obtained, so as to achieve the purpose of multi-granularity data analysis. As a representative model of granular-ball computing, granular ball neighborhood rough set model (GBNRS) offers greater generality and flexibility as it can adaptively generate different neighborhood radii for each object. However, GBNRS consistently sets the purity degree with 1 for all granular-balls, which may lead to poor fault tolerance in uncertain information systems. Additionally, GBNRS lacks effective approximation operators, making it hard to effectively characterize the differences among samples. For these reasons, a new variable- precision rough set model is set forth by combining granular-ball rough sets, fuzzy rough sets and neighborhood rough sets. To this end, a granular-ball fuzzy neighborhood is presented to reflect the similarity of the samples and a pair of variable-precision approximation operators is formulated to improve the noise-tolerant ability. On this basis, a new granular-ball rough set model i.e. fuzzy neighborhood based granular-ball rough sets (FNGBRS) is proposed. Furthermore, a variable-precision dependency function is introduced to evaluate the classification ability of a given feature sets at different granularity levels. The dimensionality reduction of decision systems is carried out under the condition of keeping the classification ability unchanged, and a feature selection algorithm is developed by using the variable-precision dependency function. Numerical experiments on 12 different types of datasets demonstrate that the proposed model outperforms some state-of-the-art feature learning algorithms in terms of classification accuracy and the number of selected features.