Publications

The concept of hierarchical models of associations of fuzzy sets (linguistic labels) is discussed. Three basic levels of hierarchy (relational, set-theoretic, and scalar) facilitate the handling of a variety of relationships between fuzzy sets. Learning mechanisms capable of discovering parameters of the models introduced are studied. The inverse problem in models of associations is formulated along with a construction of diverse forms of matching achieved there. An illustrative numerical example in pattern classification is also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Knowledge representation realized by information granules is one of the essential facets of granular computing and an area of intensive research. Fuzzy clustering and clustering are general vehicles to realize formation of information granules. Granulation - degranulation paradigm is one of the schemes determining and quantifying functionality and knowledge representation capabilities of information granules. In this study, we augment this paradigm by forming and optimizing a collection of associations among original and transformed information granules. We discuss several transformation schemes and analyze their properties. A series of numeric experiments is provided using which we quantify the improvement of the degranulation mechanisms offered by the optimized transformation of information granules.

In this study, we introduce a novel clustering architecture, in which several subsets of patterns can be processed together with an objective of finding a common structure. The structure revealed at the global level is determined by exchanging prototypes of the subsets of data and by moving prototypes of the corresponding clusters toward each other. Thereby, the required communication links are established at the level of cluster prototypes and partition matrices, without hampering the security concerns. A detailed clustering algorithm is developed by integrating the advantages of both fuzzy sets and rough sets, and a measure of quantitative analysis of the experimental results is provided for synthetic and real-world data.

Two basic issues for data analysis and kernel-machines design are approached in this paper: determining the number of partitions of a clustering task and the parameters of kernels. A distance metric is presented to determine the similarity between kernels and FCM proximity matrices. It is shown that this measure is maximized, as a function of kernel and FCM parameters, when there is coherence with embedded structural information. We show that the alignment function can be maximized according FCM and kernel parameters. The results presented shed some light on the general problem of setting up the number of partitions in a clustering task and in the proper setting of kernel parameters according to structural information. Keywords— Affinity matrix, Clustering, Fuzzy C-Means (FCM), Kernel matrix, Reordering, Sorting.

In this study, we propose a new design methodology of granular fuzzy models, introduce its further generalization in the form of granular fuzzy models of higher type, and discuss detection and characterization of outliers expressed with regard to the constructed information granules. In recent years, various models that describe the system from different perspectives have been built to resolve the growing challenges brought on by real-world systems. These models usually aim to achieve the highest accuracy at the cost of model interpretability. To improve the interpretability of models, a concept of granular models has been developed in the setting of granular computing. We focus on the formation of a general granular model at the higher level of hierarchy by taking advantage of existing models developed at the lower (numeric) level. Here, information granularity is regarded as an important design asset whose optimal allocation across the parameters of the original model gives rise to granular models. Next, through an allocation of information granularity to the existing type-1 granular model, we create an interesting and useful augmentation of the granular fuzzy model by forming a granular fuzzy model of type-2. Higher type granular models are also realized through the optimal allocation of information granularity. We examine the problem of outlier detection in granular models where outliers are expressed with regard to the constructed information granules. Experimental results demonstrate that granular fuzzy models provide significant improvement to the model's interpretability, and the proposed outlier detection method based on granular models of higher type is effective.