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Fuzzy clustering has emerged as a fundamental technique of information granulation. In this study, we introduce and discuss multivariable encoding and decoding mechanisms (referred altogether as a reconstruction problem) expressed in the language of fuzzy sets and fuzzy relations. The underlying performance index associated with the problem helps quantify a reconstruction error that arises when transforming a numeric datum through fuzzy sets (relations) and then reconstructing it into an original numeric format. The clustering platform considered in this study concerns the well-known algorithm of Fuzzy C-Means (FCM). The main design aspects deal with the relationships between the number of clusters versus the reconstruction properties and the resulting reconstruction error. The impact of the fuzzification coefficient on the reconstruction quality is investigated. This finding is of interest, given the fact that predominantly all applications involving FCM use the value of the fuzzification coefficient equal to 2. In light of the completed experiments, we demonstrate that this selection may not be experimentally. legitimate. We also carry out a comparative analysis of the reconstruction properties of the Boolean decoding that is induced by the fuzzy partition. Experimental investigations involve selected machine learning data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new design methodology that supports the development of hybrid incremental models. These models result through an iterative process in which a parametric model and a nonparametric model are combined so that their underlying and complementary functionalities become fully exploited. The parametric component of the hybrid model captures some global relationships between the input variables and the output variable. The nonparametric model focuses on capturing local input-output relationships and thus augments the behavior of the model being formed at the global level. In the underlying design, we consider linear and quadratic regression to be a parametric model, whereas a fuzzy k-nearest neighbors model serves as the nonparametric counterpart of the overall model. Numeric results come from experiments that were carried out on some low-dimensional synthetic data sets and several machine learning data sets from the University of California-Irvine Machine Learning Repository. [ABSTRACT FROM AUTHOR]