Fuzzy neighborhood Choquet integrals with overlap functions and their applications in attribute reduction

Abstract

In fuzzy rough sets, fuzzy neighborhood operators and fuzzy rough approximate operators are mainly used by traditional methods to deal with the problem of attribute reduction (i.e., feature selection). However, they are parametric linear, while the corresponding weights are additive measures. For complex data, parametric linear operators and additive measures do not reflect correlations among data (or attributes). Therefore, it is important to develop non-additive measures and nonlinear operators for attribute reduction, which can effectively find those attributes that are not needed to reach a decision from the viewpoint of correlations. Along these lines, in this work, OI-fuzzy β-neighborhood measures (i.e., non-additive measures) and generalized Choquet integrals (i.e., nonlinear integrals) are presented by using overlap functions to deal with the problem of attribute reduction under the fuzzy β-covering approximation space. First, four pairs of OI-fuzzy β-neighborhood operators are constructed based on the implementation of overlap functions and their residual implications in a fuzzy β-covering approximation space. Furthermore, four pairs of OI-fuzzy β-neighborhood measures, as non-additive measures, are introduced to instead of rough approximate operators in data mining. Then, a novel method with respect to OI-fuzzy β-neighborhood measures is presented to deal with the attribute reduction in a fuzzy β-covering information decision table. Third, four pairs of generalized Choquet integrals based on the employment of OI-fuzzy β-neighborhood measures are constructed. On top of that, another method with respect to these generalized Choquet integrals is proposed to deal with the attribute reduction in a fuzzy β-covering information decision table. Finally, the presented methods are used to deal with the problem of classification. Several public data sets are applied to illustrate the feasibility and effectiveness of the above-mentioned proposed methods.