A large number of clustering methods exist including deterministic, probabilistic, and fuzzy clustering. All these methods are devoted to handling different types of uncertainty. No studies have been encountered on clustering taking into account a confluence of probabilistic and fuzzy information. In the existing studies, the reliability of extracted knowledge is one of the important issues to be investigated. The concept ofZ-number arises as a formal construct that expresses reliability of information under bimodal distribution. In this article, we propose an approach to construction ofZ-number-valued clusters of a dataset for evaluation of reliability of extracted data-driven knowledge. Real-world applications are given that confirm the usefulness of the proposed method.

The paper analyses issues leading to errors in graphic object classifiers. The distance measures suggested in literature and used as a basis in Traditional, fuzzy, and Neuro-Fuzzy classifiers are found to be not very suitable for classification of non-stylized or fuzzy objects in which the features of classes are much more difficult to recognize because of significant uncertainties in their location and gray-levels. The authors suggest a Neuro-Fuzzy graphic object classifier with modified distance measure that gives better performance indices than systems based on traditional ordinary and cumulative distance measures. The simulation has shown that the quality of recognition significantly improves when using the suggested method.