Relevancia y calidad en sistemas de clasificación borrosaun enfoque algebraico

  1. Fabián Alberto Castiblanco Ruiz
Supervised by:
  1. Francisco Javier Montero de Juan Director
  2. Camilo Andrés Franco de los Ríos Director
  3. Juan Tinguaro Rodríguez González Director

Defence university: Universidad Complutense de Madrid

Year of defence: 2021

  1. Matilde Santos Peñas Chair
  2. Daniel Gómez González Secretary
  3. Vincenzo Cutello Committee member
  4. Fabio Augusto González Osorio Committee member
  5. Ana Isabel del Amo Blanco Committee member
  1. Estadística e Investigación Operativa

Type: Thesis


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...