Noise-tolerant feature selections are valuable for data learning; they can resort to efficient fuzzy granulations and uncertainty measures, and a fundamental model concerns weighted kernel fuzzy rough sets (WKFRSs) which consider data distributions and uncertainty. In terms of current WKFRSs, fuzzy granulations adopt k-nearest neighbors for weighted optimization, while uncertainty measures consider single algebraic and informational views; corresponding feature selection algorithms have made achievements of noisy processing, but still exist advancement space from granulation deepening and measurement reinforcement. In this paper embracing WKFRSs, two-type weight-fuzzy granulations are defined by using self-adapting radius neighborhoods, three-view uncertainty measures are comprehensively constructed from uncertainty mechanisms, so 2 × (1 + 1 + 2) = 8 heuristic algorithms of feature selections are systematically established for better noise-aware learning. At first, two improved factors of local density and boundary influence are proposed by general neighborhood characterization and statistical radius determination, and thus two sample weights emerge to adjust Gaussian-kernel fuzzy relations to induce two weight-fuzzy granulations. Then, the fuzzy precision and fuzzycomplementary mutual information are respectively proposed from algebraic and informational views, and the two are combined into two fused measures via arithmetic and geometric means. Furthermore, the above two-type granulations and threeview measures two-dimensionally generate 2×(1+1+2) = 8 new heuristic selection algorithms via feature significances. Finally by data experiments, constructional fuzzy granulations, uncertainty measures, feature selections are validated to have anti-noise characteristics and corresponding robustness, while new selection algorithms acquire better performances of classification learning than multiple contrast algorithms.

Outliers carry significant information to reflect an anomaly mechanism, so outlier detection facilitates relevant data mining. In terms of outlier detection, the classical approaches from distances apply to numerical data rather than nominal data, while the recent methods on basic rough sets deal with nominal data rather than numerical data. Aiming at wide outlier detection on numerical, nominal, and hybrid data, this paper investigates three-way neighborhood characteristic regions and corresponding fusion measurement to advance outlier detection. First, neighborhood rough sets are deepened via three-way decision, so they derive three-way neighborhood structures on model boundaries, inner regions, and characteristic regions. Second, the three-way neighborhood characteristic regions motivate the information fusion and weight measurement regarding all features, and thus, a multiple neighborhood outlier factor emerges to establish a new method of outlier detection; furthermore, a relevant outlier detection algorithm (called 3WNCROD) is designed to comprehensively process numerical, nominal, and mixed data. Finally, the 3WNCROD algorithm is experimentally validated, and it generally outperforms 13 contrast algorithms to perform better for outlier detection.