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This study is devoted to the generalization of information granules by forming higher order, namely, order-2 information granules. Information granules are semantically meaningful entities, which play a central role in knowledge representation and system modeling in the framework of Granular Computing. The encountered information granules could exhibit significant heterogeneity because of the diversified formal formalisms. To facilitate an effective generalization of heterogeneous granular data when using clustering algorithms, an efficient scheme has been proposed to form a unified representation of various types of granular data by using Possibility–necessity measures. Once the clustering process has been completed in the possibility–necessity feature space, the higher order information granules come as results of decoding by involving the possibility–necessity metrics and fuzzy relational calculus. The extent to which the higher order information granules are supported by the granular data present at a lower level of hierarchy is quantified in terms of the membership degrees obtained in the clustering process. Experimental studies concerning a series of publicly available datasets coming from UCI and KEEL machine learning repositories are carried out in this study. • A novel encoding/decoding method for representing heterogeneous granular data. • Clustering algorithm can be applied to cluster encoded heterogeneous granular data. • Supported by fuzzy relational calculus theory and Possibility-necessity measures. [ABSTRACT FROM AUTHOR]

Abstract: Information granules, such as e.g., fuzzy sets, capture essential knowledge about data and the key dependencies between them. Quite commonly, we may envision that information granules (fuzzy sets) have become a result of fuzzy clustering and therefore could be succinctly represented in the form of some fuzzy partition matrices. Interestingly, the same data set could be represented from various standpoints and this multifaceted view yields a collection of different partition matrices being reflective of the higher-order granular knowledge about the data. The levels of specificity of the clusters the data are organized into could be quite different—the larger the number of clusters, the more detailed insight into the structure of data becomes available. Given the granularity of the resulting constructs (rather than plain data themselves), one could view a collection of partition matrices as a certain type of a network of knowledge. Considering a variety of sources of knowledge encountered across the network, we are interested in forming consensus between them. In a nutshell, this leads to the construction of certain fuzzy partition matrices which “reconcile” the knowledge captured by the individual partition matrices. Given that the granularity of the sources of knowledge under consideration could vary quite substantially, we develop a unified optimization perspective by introducing fuzzy proximity matrices that are induced by the corresponding partition matrices. In the sequel, the optimization is realized on a basis of these proximity matrices. We offer a detailed algorithm and illustrate its performance using a series of numeric experiments. [Copyright &y& Elsevier]

Concept-cognitive learning (CCL), an emerging intelligence learning paradigm, has recently become a popular research subject in artificial intelligence and cognitive computing. A central notion of CCL is cognitive and learning things via concepts. In this process, concepts play a fundamental role when mining and fusing knowledge from data to wisdom. With the in-depth research and expansion of CCL in scopes, goals, and methodologies, some difficulties have gradually emerged, including some vague terminology, ambiguous views, and scattered research. Hence, a systematic and comprehensive review of the development process and advanced research about CCL is particularly necessary at the moment. This paper summarizes the theoretical significance, application value, and future development potential of CCL. More importantly, by synthesizing the reviewed related research, we can acquire some interesting results and answer three essential questions: (1) why examine a cognitive and learning framework based on concept? (2) what is the concept-cognitive learning? (3) how to make concept-cognitive learning? The findings of this work could act as a valuable guide for related studies in quest of a clear understanding of the closely related research issues around concept-cognitive learning. • It is the first paper that attempts to provide an in-depth analysis of the advancement of CCL. • It is a multi-view categorization of CCL in research scopes, goals, and methodologies. • It is an elucidation of the main research gaps and suggestions for the related study of CCL. • It acquires some interesting results by synthesizing the reviewed related research of CCL. [ABSTRACT FROM AUTHOR]

Abstract: Feature selection is a challenging problem in areas such as pattern recognition, machine learning and data mining. Considering a consistency measure introduced in rough set theory, the problem of feature selection, also called attribute reduction, aims to retain the discriminatory power of original features. Many heuristic attribute reduction algorithms have been proposed however, quite often, these methods are computationally time-consuming. To overcome this shortcoming, we introduce a theoretic framework based on rough set theory, called positive approximation, which can be used to accelerate a heuristic process of attribute reduction. Based on the proposed accelerator, a general attribute reduction algorithm is designed. Through the use of the accelerator, several representative heuristic attribute reduction algorithms in rough set theory have been enhanced. Note that each of the modified algorithms can choose the same attribute reduct as its original version, and hence possesses the same classification accuracy. Experiments show that these modified algorithms outperform their original counterparts. It is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets. [Copyright &y& Elsevier]