Special Issue on Granular Knowledge Discovery

Granular Computing becomes increasingly popular in modeling of intelligent systems. Granulation of information is inherent in human thinking and reasoning processes. Granular Computing provides an information processing framework where interactive computation and operations are performed on information granules, and is based on the realization that precision is sometimes expensive and/or not much meaningful in modeling and controlling complex systems. When a problem involves incomplete, uncertain, and vague information, it can be difficult or infeasible to differentiate distinct elements. Therefore, one can find it convenient to consider granules for such problem’s handling. Moreover, this may lead to more efficient approximate reasoning supporting the decision processes. This special issue aims at presenting the state of the art in foundations and applications of Granular Computing. As important trends in applications, we consider the Knowledge Discovery in Databases and the Decision Support Systems. In both these areas, data and knowledge granulation lead to more robust models and processes, more meaningful interaction with domain experts and more efficient cooperation between different layers of complex systems. In particular, granulation on different layers can result in generation of relevant (e.g., for classification) structured objects and patterns over such objects. Thus, it is important to conduct research on how to discover granules from data and how to utilize them to represent highlevel concepts in decision support mechanisms. From this perspective, we proposed to entitle this issue as the special issue on Granular Knowledge Discovery. The issue consists of seven papers. Paper submissions were gathered on invitation basis. An open call for special issue contributions was announced as well. Submissions were carefully peer-reviewed by independent experts, with two evaluation reports per manuscript. Revised versions of pre-accepted papers were reexamined to assure that all recommended changes and extensions were introduced. The first paper, by Hiroshi Sakai, Mao Wu, Naoto Yamaguchi and Michinori Nakata, is titled “Granules for Association Rules and Decision Support in the getRNIA System”. The authors work with granules gathering objects supporting components of association rules derived from non-deterministic information systems, which can reflect data sources with missing values, set values or interval values. While taking a form of easy-to-handle blocks for classical data sets, granules of objects supporting association rules become more complex if incompleteness, inexactness and uncertainty are involved. Nevertheless, the authors show that association rules can be learnt using computations on granules even for such non-standard, nondeterministic data. The appropriately designed Granular Computing framework is implemented within the getRNIA decision support system developed by the authors. The second paper, by Witold Pedrycz, is titled “Granular Fuzzy Rule-Based Architectures: Pursuing Analysis and Design in the Framework of Granular Computing”. The author studies granular rule-based models whose rules assume a format “if G(. . . ) then G(. . . )”, where G(. . . ) denotes granular generalizations of numeric conditions and conclusions. Generalizations can be expressed, e.g., in terms of interval-valued, type-2 or probabilistic fuzzy sets. The author discusses and motivates several classes of fuzzy models depending on available information granules. The design of granular architectures exploits principles of justifiable granularity and optimal allocation of information granularity. Performance indexes of rules are thoroughly studied as well. Like in the case of the first paper, this research utilizes granular models to deal with complex real-world data sets.