A Generalization of the k-means Algorithm for Clustering Data Based on Fuzzy Population

Articles in Press

Document Type : Research Paper

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Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

‎Clustering is one of the data mining tools frequently used in multivariate methods to group observations into clusters based on the similarity of variables‎. ‎While many clustering algorithms have been developed for data extracted from well-defined (crisp) populations‎, ‎numerous real-world problems involve inherently fuzzy populations such as high-consumption households or high-quality products‎. ‎In such cases‎, ‎each data point is described not only by its observed values but also by its degree of membership to the fuzzy population‎. ‎This study proposes a novel clustering algorithm specifically designed for data extracted from fuzzy populations‎. ‎The proposed method generalizes the classical k-means algorithm by considering membership degrees in the clustering process‎. ‎The effectiveness of the proposed algorithm was evaluated on both synthetic and real-world datasets using several validity indices‎. ‎According to these indices‎, ‎the algorithm demonstrates satisfactory clustering quality and computational efficiency‎. The analysis of the proposed algorithm in the presence of outliers shows that, although outliers can slightly shift cluster centers, the overall clustering structure remains stable when clusters are well-separated.

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Iranian Journal of Fuzzy Systems

Articles in Press, Accepted Manuscript
Available Online from 23 May 2026

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