Concept-cognitive learning is an emerging area of cognitive computing, which refers to continuously learning new knowledge by imitating the human cognition process. However, the existing research on concept-cognitive learning is still at the level of complete cognition as well as cognitive operators, which is far from the real cognition process. Meanwhile, the current classification algorithms based on concept-cognitive learning models (CCLMs) are not mature enough yet since their cognitive results highly depend on the cognition order of attributes. To address the above problems, this article presents a novel concept-cognitive learning method, namely, stochastic incremental incomplete concept-cognitive learning method (SI2CCLM), whose cognition process adopts a stochastic strategy that is independent of the order of attributes. Moreover, a new classification algorithm based on SI2CCLM is developed, and the analysis of the parameters and convergence of the algorithm is made. Finally, we show the cognitive effectiveness of SI2CCLM by comparing it with other concept-cognitive learning methods. In addition, the average accuracy of our model on 24 datasets is 82.02%, which is higher than the compared 20 classification algorithms, and the elapsed time of our model also has advantages.

As one of the most important concepts for classification learning, neighborhood granules obtained by dividing adjacent objects or instances can be regarded as the minimal elements to simulate human cognition. At present, neighborhood granules have been successfully applied to knowledge acquisition. Nevertheless, little work has been devoted to the simultaneous selection of features and instances by the use of neighborhood granules. To fill this gap, we investigate in this paper the issue of bi-selection of instances and features based on neighborhood importance degree (NID). Firstly, the conditional neighborhood entropy is defined to measure decision uncertainty of a neighborhood granule. Considering both decision uncertainty and coverage ability of a neighborhood granule, we propose the concept of NID. Then, an instance selection algorithm is formulated to select representative instances based on NID. Furthermore, an NID-based feature selection algorithm is provided for a neighborhood decision system. By integrating the instance selection and feature selection methods, a bi-selection approach based on NID (BSNID) is finally proposed to select instances and features. Lastly, some numerical experiments are conducted to evaluate the performance of BSNID. The results demonstrate that BSNID can take account of both reduction ratio and classification accuracy and, therefore, performs satisfactorily in effectiveness.

As a powerful tool for the representation of classifying knowledge, fuzzy classification rules can not only effectively deal with imprecise and uncertain data, but also possess readability and interpretability. Fuzzy granular rules, also to be a kind of fuzzy classification rules, can be induced by fuzzy information granules. It has been acknowledged that one of the important criteria for evaluating the quality of information granules comes from the principle of justifiable granularity. Unfortunately, the existing methods for extracting fuzzy granular rules fail to take into account the principle of justifiable granularity. In view of the advantages of the justifiable granularity principle in classifying knowledge, we propose in this article a new method of extracting fuzzy granular rules using the justifiable granularity principle and a fusion strategy and establish a fuzzy granular rule-based classifier (FGRBC). Specifically, the justifiability of fuzzy granules is first presented according to both coverage and specificity of fuzzy granules, on which a rule extraction method is formulated to obtain a set of fuzzy granular rules. Furthermore, a fusion strategy is put forward to generate a set of fused rules. Then, the two sets of rules are combined and attribute reduction is performed on the combined rule set. Finally, the reduced combined rule set is employed to construct FGRBC. Moreover, performance of FGRBC is evaluated by numerical experiments and the results show that FGRBC is of satisfactory classification ability.

Data reduction, aiming to reduce the original data by selecting the most representative information, is an important technique of preprocessing data. At present, large-scale or huge data are very common and the development of data reduction techniques for such data has attracted much attention. As a powerful tool for handling uncertainty in real-valued data, the fuzzy rough set theory has been widely applied to data reduction including extensive feature selection methods and some instance selection approaches. Nevertheless, not much work has been devoted to the simultaneous selection of feature and instance based on fuzzy rough sets. In this article, we investigate the fuzzy rough set-based bi-selection issue for data reduction. Specifically, the unified concepts of the importance degrees of fuzzy granules are presented to select the representative instances first and then the critical features. An instance selection algorithm with a noise elimination technique is provided to firstly remove the noise and then select the representative instances according to the importance degrees of fuzzy granules. Then, the importance-degree-preserved attribute reduction is proposed, and a corresponding feature selection algorithm with a wrapper technique is given to search for a best feature subset. Last, the bi-selection method based on fuzzy rough sets (BSFRS) is presented for data reduction by integrating the instance selection and the feature selection methods. Moreover, some numerical experiments are conducted to assess the performance of BSFRS, and the results show that BSFRS performs well in terms of the effectiveness.

Feature selection is a popular technique of preprocessing data. In order to deal with dynamic or large data, incremental feature selection has been developed, in which the features selected from existing data are integrated with those mined from both existing and dynamic data in the manner of incremental computation. Fuzzy rough set theory is powerful in handling uncertainty in real-valued data or even mixed data, and one of its most important applications is feature selection. Nevertheless, not much work has been found on fuzzy-rough-set-based incremental feature selection. Therefore, in this article, we investigate the incremental feature selection using a fuzzy-rough-set-based information entropy with incoming instances. Specifically, the representative instances from the incoming ones are first selected according to the information coverage of fuzzy granules generated by fuzzy rough sets. Then, the incremental mechanism of the fuzzy-rough-set-based information entropy is formulated by adding newcome instances. Finally, an incremental feature selection procedure, which we call active incremental feature selection, is proposed. Furthermore, some numerical experiments are conducted to assess the performance of the proposed feature selection algorithm, and the results show that our algorithm is of a prominent advantage in terms of computational time, especially for a dataset with large number of instances.

Attribute reduction is the strongest and most characteristic result in rough set theory to distinguish itself to other theories. In the framework of rough set, an approach of discernibility matrix and function is the theoretical foundation of finding reducts. In this paper, sample pair selection with rough set is proposed in order to compress the discernibility function of a decision table so that only minimal elements in the discernibility matrix are employed to find reducts. First relative discernibility relation of condition attribute is defined, indispensable and dispensable condition attributes are characterized by their relative discernibility relations and key sample pair set is defined for every condition attribute. With the key sample pair sets, all the sample pair selections can be found. Algorithms of computing one sample pair selection and finding reducts are also developed; comparisons with other methods of finding reducts are performed with several experiments which imply sample pair selection is effective as preprocessing step to find reducts.