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.

Granular computing (GrC) and two-way concept learning (TCL) are influential studies of knowledge processing and cognitive learning. A central notion of two-way concept learning is learning concepts from an arbitrary information granule. Although TCL has been widely adopted for concept learning and formal concept analysis in a fuzzy context, the existing studies of TCL still have some issues: 1) the sufficient and necessary granule concept is only obtained from the necessary granule or sufficient granule concept; 2) the cognitive mechanism ignores integrating past experiences into itself to deal with dynamic data. Meanwhile, concept-cognitive learning (CCL) method still faces challenges, such as incomplete cognitive and weak generalization ability. This paper proposes a novel two-way concept-cognitive learning method for dynamic concept learning in a fuzzy context for these problems and challenges. Unlike TCL, fuzzy-based twoway concept-cognitive learning (F-TCCL) is more flexible and less time-consuming to learn granule concepts from the given clue, and meanwhile, it is good at dynamic concept learning. Moreover, we design a fuzzy-based progressive learning mechanism within this framework under the dynamic environment. Some numerical experiments on public datasets verify the effectiveness of our proposed method. The considered framework can provide a convenient novel method for researching two-way learning and concept-cognitive learning.

Concept-cognitive learning (CCL) and three-way decision (3WD) models provide powerful techniques for knowledge discovery. Some early attempts in the field have successfully combined CCL and 3WD, i.e., three-way concept learning. However, only a few attempts were made to combine CCL with 3WD in a dynamic fuzzy context due to two challenges: 1) three-way concept-cognitive learning incapability; 2) the current incremental three-way concept learning mechanism is insufficient to model real-time updating cognitive procedure. Hence, this paper first shows some new standpoints on improving fuzzy based CCL accuracy and then proposes fuzzy-granular three-way concept-cognitive learning (F3WG-CCL) for concept modeling and dynamic knowledge learning. Specifically, we first define a new F3WG-concept to characterize the knowledge embedded in fuzzy data. Furthermore, a big concept priority principle and an update mechanism are borrowed for concept recognition and dynamic concept cognition. Finally, we show that F3WG-CCL can be implemented simultaneously via theoretical guarantee and sufficient experimental, including 1) achieving state-of-the art dynamic knowledge learning; 2)demonstratingthatthethreeway concept is effective in a fuzzy context; 3) discovering that the big concept is valuable for fuzzy concept recognition. Our work will provide a powerful approach to research fuzzy-based CCL and dynamic knowledge discovery

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.

Representation and learning of concepts are critical problems in data science and cognitive science. However, the existing research about concept learning has one prevalent disadvantage: incomplete and complex cognitive. Meanwhile, as a practical mathematical tool for concept representation and concept learning, two-way learning (2WL) also has some issues leading to the stagnation of its related research: the concept can only learn from specific information granules and lacks a concept evolution mechanism. To overcome these challenges, we propose the two-way concept-cognitive learning (TCCL) method for enhancing the flexibility and evolution ability of 2WL for concept learning. We first analyze the fundamental relationship between two-way granule concepts in the cognitive system to build a novel cognitive mechanism. Furthermore, the movement three-way decision (M-3WD) method is introduced to 2WL to study the concept evolution mechanism via the concept movement viewpoint. Unlike the existing 2WL method, the primary consideration of TCCL is two-way concept evolution rather than information granules transformation. Finally, to interpret and help understand TCCL, an example analysis and some experiments on various datasets are carried out to demonstrate our method’s effectiveness. The results show that TCCL is more flexible and less time-consuming than 2WL, and meanwhile, TCCL can also learn the same concept as the latter method in concept learning. In addition, from the perspective of concept learning ability, TCCL is more generalization of concepts than the granule concept cognitive learning model (CCLM).