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.
By 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 extends the h‑plot multidimensional scaling technique to handle three‑way asymmetric dissimilarities, enabling the extraction of archetypal profiles and clustering in a unified Euclidean space. It provides an explicit eigenvector‑based solution that avoids local minima, is scale‑invariant, computationally efficient, and includes a straightforward goodness‑of‑fit assessment. The method is benchmarked against existing models and demonstrated on a financial dataset, with all data and code made publicly available for reproducibility.
By Mireia Mollar-Gumbau, Aleix Alcacer, Rafael Benitez, Vicente J. Bolos, Irene Epifanio
arXiv:2609. 20194v1 Announce Type: cross Abstract: Triangular membership functions (MFs) are widely used in fuzzy systems because of their interpretability, low parameterization complexity, and strong locality properties.
By Babak Sarani, Rahman Ardakanian, Ali Mousavi
arXiv:2511.09801v3 Announce Type: replace-cross
Abstract: This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by inc...
By Salvish Goomanee, Andi Han, Pratik Jawanpuria, Bamdev Mishra
arXiv:2607. 05464v1 Announce Type: cross Abstract: The success of categorical data clustering generally much relies on the distance metric that measures the dissimilarity degree between two objects.
By Yiqun Zhang, Yiu-ming Cheung
arXiv:2608. 11768v1 Announce Type: new Abstract: The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning.
By Haoran Pei, Zhao Su, Zetao Lin, Haoran Li, Jun Shen, Qi Zhu, Lan Guo, Qingguo Zhou, Binbin Yong