Publication: Relevancia y Calidad en Sistemas de Clasificación Borrosa. Un Enfoque Algebraico
Loading...
Files
Official URL
Full text at PDC
Publication Date
2021-07-26
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Complutense de Madrid
Citations
Exportar
Abstract
La validación de clústeres borrosos es un problema abierto y con varias perspectivas para su estudio. La presente tesis doctoral aborda el problema de determinarla calidad de particiones borrosas en procesos de clasificación no supervisada. Para tal objetivo, se han propuesto criterios e índices que permiten determinar particiones borrosas de calidad y de alta calidad, la relevancia de una clase o familia de clases en una partición borrosa dada y, el número óptimo de clases de una partición de acuerdo a algunas características estudiadas. La propuesta establecida, emplea herramientas provenientes del álgebra abstracta como son, la teoría de grupos, particularmente la teoría de subgrupos borrosos, matrices de relaciones y los polinomios característicos de tales matrices. Los resultados teóricos fueron aplicados y validados en el problema de segmentación de imágenes...
Fuzzy cluster validation is an open problem with several perspectives for study. This doctoral thesis addresses the problem of determining the quality of fuzzy partitionsin unsupervised classification processes. For this purpose, criteria and indexes have been proposed that allow determining quality and high-quality fuzzy partitions, the relevance of a class or family of classes in a given fuzzy partition and, the optimal number of classes of a partition according to some characteristics studied.The proposal uses tools from abstract algebra such as group theory, particularly the theory of fuzzy subgroups, matrices of relations and the characteristic polynomials of such matrices. The theoretical results were applied and validated in the image segmentation problem...
Fuzzy cluster validation is an open problem with several perspectives for study. This doctoral thesis addresses the problem of determining the quality of fuzzy partitionsin unsupervised classification processes. For this purpose, criteria and indexes have been proposed that allow determining quality and high-quality fuzzy partitions, the relevance of a class or family of classes in a given fuzzy partition and, the optimal number of classes of a partition according to some characteristics studied.The proposal uses tools from abstract algebra such as group theory, particularly the theory of fuzzy subgroups, matrices of relations and the characteristic polynomials of such matrices. The theoretical results were applied and validated in the image segmentation problem...
Description
Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 26/01/2021