arXiv Machine LearningBy Inmaculada Guti\'errez (Faculty of Statistical Studies, Complutense University of Madrid, Instituto Universitario de Estad\'istica y Ciencia de Datos, Complutense University of Madrid), Asier Urio-Larrea (Department of Statistics, Computer Science and Mathematics, Universidad P\'ublica de Navarra, Institute of Smart Cities), J. Tinguaro Rodr\'iguez (Faculty of Mathematics, Complutense University of Madrid, Instituto de Matem\'atica Interdisciplinar, Complutense University of Madrid), Daniel G\'omez (Faculty of Statistical Studies, Complutense University of Madrid, Instituto Universitario de Estad\'istica y Ciencia de Datos, Complutense University of Madrid), Javier Montero (Faculty of Mathematics, Complutense University of Madrid, Instituto de Matem\'atica Interdisciplinar, Complutense University of Madrid), Humberto Bustince (Department of Statistics, Computer Science and Mathematics, Universidad P\'ublica de Navarra, Institute of Smart Cities)
The paper introduces the concept of matrix aggregation operators (MAOs), a formal framework for aggregating data naturally arranged in matrices, such as membership degrees in fuzzy systems. It examines properties like decomposability and symmetry, showing that some MAOs cannot be expressed in decomposable form. The authors also propose a new family of MAOs called maximum entropy global coverage indices (MEGCIs), constructed from grouping functions and MEOWA operators, and demonstrate their effectiveness in assessing cluster quality through extensive experiments.
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arXiv:2604. 23628v2 Announce Type: replace-cross Abstract: Hierarchical clustering is a fundamental task in data analysis, but classical methods have long lacked a principled objective function.
arXiv:2608. 19234v1 Announce Type: new Abstract: Decision-making in complex systems often involves dealing with imprecise or uncertain information, frequently represented using fuzzy sets, particularly Triangular Fuzzy Numbers (TFNs).
By Eddy Soria, Aida Valls, Ana Beatriz Hern\'andez-Lara
The paper introduces absolute cluster indices that assess both compactness and separability of clusters, moving beyond relative measures commonly used in clustering validation. It defines a compactness function for each cluster and a set of neighboring points for cluster pairs to evaluate cluster quality and overall distribution margin. These indices are applied to determine the true number of clusters and are compared against widely-used validity indices on synthetic and real-world datasets.
By Adil M. Bagirov, Ramiz M. Aliguliyev, Nargiz Sultanova, Sona Taheri
arXiv:2607. 23243v1 Announce Type: new Abstract: Fuzzy Integral (FI) based aggregation provides a powerful mechanism for nuanced aggregation, for example, in ensemble approaches or decision-level fusion more generally.
arXiv:2111. 15255v2 Announce Type: replace-cross Abstract: The probabilistic linguistic term has been proposed to deal with probability distributions in provided linguistic evaluations.
The paper investigates whether the impossibility results for flat clustering—specifically Kleinberg’s axioms of scale invariance, richness, and consistency—extend to hierarchical clustering. It demonstrates that, unlike the flat case, there exist uncountably many hierarchical clustering methods that satisfy all three axioms, termed admissible methods. The authors construct several such methods, explore a refinement partial order among them, and show that while the set of admissible methods is diverse, every method shares a common backbone of well‑separated clusters.