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Rules in fuzzy rule-based models convey essential knowledge about the system under discussion. As such, they capture the essence of relationships occurring among input and output variables. While the quality of such fuzzy models is predominantly related with the accuracy and eventual interpretability of rules (although to a limited extent), the quality of rules being regarded as generic pieces of knowledge has not been studied so far. In this study, we formulate and investigate this problem by looking at the quality of rules, including aspects of (a) stability, (b) generalizability, and (c) conflict. We identify a concept of rule multiplicity, conflict, and study an emergence of rule generalization. A number of pertinent performance indices are developed, and their usage is presented through a series of experimental studies. [ABSTRACT FROM AUTHOR]

Abstract: Semi-supervised (or partial) fuzzy clustering plays an important and unique role in discovering hidden structure in data realized in presence of a certain quite limited fraction of labeled patterns. The objective of this study is to investigate and quantify the effect of various distance functions (distances) on the performance of the clustering mechanisms. The underlying goal of endowing the clustering algorithms with a higher level of flexibility is done via the use of various distances. The enhancement of this character is evaluated by means of a comprehensive assessment of quality of clusters, their ensuing discrimination abilities and the accuracy of clusters themselves. In addition to the standard Euclidean distance being commonly exploited in fuzzy clustering, three more versatile and adaptive distance measures are considered such as its weighted version, a full adaptive distance, and a kernel-based distance. Using Fuzzy C-Means (FCM) coming in its generic format, we show its semi-supervised enhancements, derive detailed formulas and analyze their effectiveness. The improvements of semi-supervised clustering are empirically evaluated and numerically quantified with the use of several Machine Learning data sets. [Copyright &y& Elsevier]