Acquisition of<i>Z</i>-Number-Valued Clusters by Using a New Compound Function

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 of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -number arises as a formal construct that expresses reliability of information under bimodal distribution. In this article, we propose an approach to construction of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -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.