A Universal neighbourhood rough sets model for knowledge discovering from incomplete heterogeneous data

Abstract

Neighbourhood rough set theory has proven already, as an efficient tool for knowledge discovering from heterogeneous data.However, some types of the data are incomplete and noisy in practical environments, such as signal analysis, fault diagnosis etc. To solve this problem, a universal neighbourhood rough sets model (variable precision tolerance neighbourhood rough sets [VPTNRS] model) is proposed based on a tolerance neighbourhood relation and the probabilistic theory. The proposed model can be inducing a family of much more comprehensive information granules to characterize arbitrary concepts in complex universe. In this paper, we discussed the properties of the model as well as some important relevant theorems are also introduced and proved. Furthermore, a heuristic heterogeneous feature selection algorithm is given based on the model. The experimental results with 10 choices University of California Irvine (UCI) standard data sets showed that the universal model performed well both in feature selection and classification, especially in incomplete environment.

Kernel Neighborhood Rough Sets Model and Its Application

“…In this section, we select KRS [5], NRS [22], and neighborhood entropy (NE) [28] as the comparison models with KNRS. The feature subsets that are selected by different algorithms are presented in Table 5.…”

“…Based on neighborhood granulation, samples are constructed as a family of neighborhood granules to approximate the object sets. The neighborhood model can handle noisy data well based on the tolerance neighborhood relation and probabilistic theory [22]. However, the main limitation of this model is that it cannot describe the fuzziness of samples [16].…”

Rule induction based on rough sets from information tables having continuous domains

“…One approach is to use the same way as that applied to nominal attributes by Kryszkiewicz [6]. The approach is most frequently used [7–10], but it produces poor results from loss of information [11, 12]. This is because the approach fixes the indiscernibility of an object characterised by incomplete information with another object.…”

Multi-Granulation Entropy and Its Applications

“…To deal with nominal attributes and numerical attributes, which are common in practice, we use a extended Euclidean distance as the method introduced in literature [13]. This distance function is computed as follows:…”

“…Xu et al [9] proposed another generalized version, called variable precision multi-granulation rough set. There are two essential problems to be addressed when employing the rough sets model to real-world applications as similar as the information entropy model: (1) information granulation [10,11]; (2) approximate classification realized in the presence of such induced information granules [12,13]. The idea of multi-granulation is expressed through the approximation classification realizing.…”