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In this paper, we study covering-based multigranulation decision-theoretic rough sets in a multi-covering space. From viewpoints of granule, we propose the notions of covering-based mean multigranulation decision-theoretic rough sets, covering-based optimistic multigranulation decision-theoretic rough sets and covering-based pessimistic multigranulation decision-theoretic rough sets, realized, on the basis of Bayesian decision procedure. We first investigate some basic properties of those models. Then, we investigate the relationships between the proposed covering-based multigranulation decisiontheoretic rough set models and other related rough set models. Thirdly, we elaborate on the interrelationships among the proposed models. Finally, an example is employed to illustrate the application of the proposed models. [ABSTRACT FROM AUTHOR]

Anomalies are subsequences that exhibit departures from normal state of operation. In this paper, to solve the problems of unknown data distribution, control limit determination, multiple parameters, training data and fuzziness of 'anomaly', a self-adaptive and unsupervised model is developed for finding anomalies in data streams. A salient feature is a synergistic combination of both statistical and fuzzy set-based techniques. Anomaly detection problem is viewed as a certain statistical hypothesis testing which is realized in an unsupervised mode. At the same time, 'anomaly' is a much more complex concept and as such can be described with fuzzy set theory. Fuzzy sets bring a facet of robustness to the overall scheme and play an important role in the successive step of hypothesis testing. Because of the fuzzification, parameters determination is self-adaptive and no parameter needs to be specified by the user, what's more, there is no need to consider the data distribution in statistical hypothesis testing in this paper. The approach is validated with a number of experiments, which help to quantify the performance of constructed algorithm. [ABSTRACT FROM AUTHOR]

As a new and meaningful extension of the Pawlak rough set, multi-granulation rough sets (MGRSs) have attracted much attention and fruitful achievements have been reported in different aspects. By combining with fuzzy rough set, the paper introduces multi-granulation fuzzy rough sets in the covering approximation space, namely, covering-based multi-granulation fuzzy rough sets (CMFRS), which form the extension of fuzzy rough sets. We first investigate several important properties of lower and upper approximations of concepts in covering-based multi-granulation fuzzy rough sets and elaborate on the differences between the proposed models and the existing ones in literature. By employing the notions of reduct and exclusion of a covering, the paper studies the necessary and sufficient conditions for two CMFRS to generate identical lower and upper approximations of a target concept in the given covering approximation space. Finally, the relationships between the new models are explored in the paper. [ABSTRACT FROM AUTHOR]

Fuzzy clustering forms a cornerstone of fuzzy (granular) modeling. The clusters (prototypes) are viewed as a blueprint of the model that is further refined through a number of detailed estimation techniques. In this study, we claim that while clustering is indisputable essential to fuzzy modeling, the essence of clustering mechanisms supporting this process of information granulation is not compatible with the character of the task at hand. In modeling, the required constructs are inherently direction-sensitive (that is we clearly distinguish between input and output variables). On the other hand, fuzzy clustering is direction neutral and during the formation of the clusters does not take this into consideration. We re-formulate the clustering so that the directionality aspect can be addressed in the optimization process. This leads to a new, augmented objective function to be minimized. A detailed algorithm is derived. As the directional sensitivity of the clustering method gives rise to different numbers of clusters in the input and output space, it becomes necessary to identify a mapping between these clusters which in turn gives rise to some allocation problem. Because of its inherently combinatorial character, the proposed solution is obtained through some genetic optimization. Comprehensive experiments demonstrate the performance of the approach and compare it with some of the generic version of the FCM clustering. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new category of fuzzy inference systems based on data (information) granulation and show their applications to the identification of complex and usually nonlinear systems. Information granules are treated as collections of objects (data, in particular) brought together by the criteria of proximity, similarity, or functionality. The formal framework of information granulation along with the information granules themselves become an important design feature of fuzzy models, which in essence are geared towards capturing relationship between information granules rather than plain numeric data. The key characteristics of experimental data being used in the construction of the fuzzy model are carefully reflected by fuzzy rules formed therein. Information granulation realized with the aid of Hard C-Means (HCM) clustering helps determine the initial values of the parameters of the fuzzy models. This in particular concerns such important components of the rules as the initial apexes of the membership functions standing in the premise part of the fuzzy rules and the initial values of the polynomial functions present in their consequence part. The initial values of the parameters are tuned effectively with the aid of the genetic algorithms (GAs) and the least square method (LSM). An aggregate objective function is constructed in order to strike a sound balance between the approximation and generalization capabilities of the fuzzy model. The model is evaluated with the use of numerical experimentation and contrasted with the quality of some "conventional" fuzzy models already encountered in the literature. [ABSTRACT FROM AUTHOR]