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Rule-based models are applicable to model the behavior of complex and nonlinear systems. Due to limited experience and randomness involving constructing information granules, an insufficient credible rules division could reduce the model’s accuracy. This paper proposes a new rule-based modeling approach, which utilizes density-based spatial clustering of applications with noise (DBSCAN)-based information granules to construct the rules. First, bear in mind the advantages of density-based clustering, DBSCAN is proposed to generate data structures. Based on these data structures, two rule-based models are constructed: 1) models using DBSCAN clusters to construct granules and rules directly and 2) models generating subgranules in each DBSCAN cluster for rule formation. Experiments involving these two models are completed, and obtained results are compared with those generated with a traditional model involving fuzzy C-means-based granules. Numerical results show that the rule-based model, which builds rules from subgranules of DBSCAN structures, performs the best in analyzing system behaviors. [ABSTRACT FROM AUTHOR]

The study is concerned with a description of large numeric data with the aid of building a limited collection of representative information granules with the objective of capturing the structure of the original data. The proposed development scheme consists of two steps. First, a clustering algorithm characterized by high flexibility of coping with the diverse geometry of data structure and efficient computational overhead is invoked. At the second step, a clustering algorithm applied to the clusters already formed during the first phase, yielding a collection of numeric prototypes is involved and the numeric prototypes produced there are then generalized into their granular prototypes. The quality of granular prototypes is quantified while their build-up is supported by the mechanisms of granular computing such as the principle of justifiable granularity. In this paper, the clustering algorithms of DBSCAN and fuzzy ${C}$ -means were used in successive phases of the processed approach. The experimental studies concerning synthetic data and publicly available data are covered and the performance of the developed approach is assessed along with a comparative analysis. [ABSTRACT FROM AUTHOR]

Big data with a large number of observations (samples) have posed genuine challenges for fuzzy clustering algorithms and fuzzy C-means (FCM), in particular. In this article, we propose an original algorithm referred to as a hyperplane division method to split the entire data set into disjoint subsets. By disjoint subsets, we mean that the data subspaces (parts of the entire data space), each of which is supported or spanned by the data points in the corresponding subset, do not overlap each other. The disjoint subsets turned out to be beneficial to the improvement of the quality of the clusters formed by the clustering algorithms. Moreover, considering that either a large number (say, thousands) or a small number (say, a few) of clusters may be pursued in the clustering task, we propose corresponding strategies (based on the hyperplane division method) to make clustering processes feasible, efficient, and effective. By validating the proposed strategies on both synthetic and publicly available data, we show their superiority (in terms of both efficiency and effectiveness) manifested in a visible way over the method of clustering the entire data and over some representative big data clustering methods. [ABSTRACT FROM AUTHOR]

In this study, we discuss a design of fuzzy associative structures (memories) realized within the framework of fuzzy clustering. Associative memories are inherently direction-free structures (and the recall of objects can be realized for any variable or a subset of variables). Fuzzy clustering being direction-free comes here as a sound design alternative. Two recall proposals are studied: one involves prototypes (being the key descriptors of the structure of the data) and their activation in the presence of partially available data to be recalled whereas the second proposal involves fuzzy correlation matrices and in principle exhibits some resemblance with a standard correlation associative memories. In the setting of associative memories, Fuzzy C-Means (FCM) is studied. The recall error is discussed with regard to the essential parameters of the FCM (the number of clusters and the fuzzification coefficient). Furthermore we discuss an optimization of the distance function used in the clustering algorithm realized with regard to the recall error. Experimental results are provided along with a comparative study involving correlation-based associative memories. [ABSTRACT FROM AUTHOR]

In this study, we introduce a concept of hierarchical granular clustering and establish its algorithmic framework. We show that the proposed model naturally gives rise to information granules that are both of higher order and higher type, offering a compelling justification behind their emergence. In a concise way, we can capture the overall architecture of information granules as a hierarchy exhibiting conceptual layers of increasing abstraction: numeric data → information granules → information granules of type-2, order-2 → … information granules of higher type/order. The elevated type of information granules is reflective of the visible hierarchical facet of processing and the inherent diversity of the individual locally revealed structures in data. While the concept and the methodology deliver some general settings, the detailed algorithmic aspects are discussed in detail when using fuzzy clustering realized by means of fuzzy c-means. Furthermore, for illustrative purposes, we mainly focus on interval-valued fuzzy sets and granular interval fuzzy sets arising at the higher level of the hierarchy. Higher type fuzzy sets are formed with the help of the principle of justifiable granularity. The conceptually sound hierarchy is established in a general way, which makes it equally applicable to various formalisms of representation of information granules. Experiments are reported for synthetic and publicly available datasets. [ABSTRACT FROM AUTHOR]

Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules–clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure. By invoking the granulation–degranulation scheme, we design granular prototypes being reflective of the structure of data to a higher extent than the representation that is provided by their numeric counterparts (prototypes). The design is formulated as an optimization problem, which is guided by the coverage criterion, meaning that we maximize the number of data for which their granular realization includes the original data. The granularity of the prototypes themselves is treated as an important design asset; hence, its allocation to the individual prototypes is optimized so that the coverage criterion becomes maximized. With this regard, several schemes of optimal allocation of information granularity are investigated, where interval-valued prototypes are formed around the already produced numeric representatives. Experimental studies are provided in which the design of granular prototypes of interval format is discussed and characterized. [ABSTRACT FROM AUTHOR]