The main task of granular computing (GrC) is about representing, constructing, and processing information granules. Information granules are formalized in many different approaches. Different formal approaches emphasize the same fundamental facet in different ways. In this paper, we propose a novel GrC method of machine learning by using formal concept description of information granules. Based on information granules, the model and mechanism of two-way learning system is constructed in fuzzy datasets. It is addressed about how to train arbitrary fuzzy information granules to become necessary, sufficient, and necessary and sufficient fuzzy information granules. Moreover, an algorithm of the presented approach is established, and the complexity of the algorithm is analyzed carefully. Finally, to interpret and help understand the theories and algorithm, a real-life case study is considered and experimental evaluation is performed by five datasets from the University of California-Irvine, which is valuable for applying these theories to deal with practical issues.

Feature selection based on neighborhood rough set is a noteworthy step in dealing with numerical data. Information entropy, proven in many theoretical analysis and practical applications, is a compelling feature evaluation method for uncertainty information measures. Nonetheless, information entropy replaces probability with uncertainty measure to evaluate the average amount of information and ignores the decision distribution of data, especially in describing the uncertainty in imbalanced data. This paper discusses an emerging method for the feature selection in fuzzy data with imbalanced data by presenting a local composite entropy based on a neighborhood rough set. Based on the neighborhood rough set model, we discuss a similar relation to describe the relationship between different objects in unbalanced fuzzy data. In this process, to fully consider the distribution characteristics of unbalanced data, we construct a local composite entropy for handling the fuzzy decision systems with uncertainty and decision distribution, which is proven to be monotonic. Moreover, to improve the selection efficiency, a local heuristic forward greedy selection algorithm based on the local composite measure is designed to select the optimal feature subset. Finally, experimental results on twelve public datasets demonstrate that our method has better classification performance than some state-of-the-art feature selection methods in fuzzy data.

Dominance-based rough approximation discovers inconsistencies from ordered criteria and satisfies the requirement of the dominance principle between single-valued domains of condition attributes and decision classes. When the ordered decision system (ODS) is no longer single-valued, how to utilize the dominance principle to deal with multivalued ordered data is a promising research direction, and it is the most challenging step to design a feature selection algorithm in interval-valued ODS (IV-ODS). In this article, we first present novel thresholds of interval dominance degree (IDD) and interval overlap degree (IOD) between interval values to make the dominance principle applicable to an IV-ODS, and then, the interval-valued dominance relation in the IV-ODS is constructed by utilizing the above two developed parameters. Based on the proposed interval-valued dominance relation, the interval-valued dominance-based rough set approach (IV-DRSA) and their corresponding properties are investigated. Moreover, the interval dominance-based feature selection rules based on IV-DRSA are provided, and the relevant algorithms for deriving the interval-valued dominance relation and the feature selection methods are established in IV-ODS. To illustrate the effectiveness of the parameters variation on feature selection rules, experimental evaluation is performed using 12 datasets coming from the University of California-Irvine (UCI) repository.