Affiliations: [a] Faculty of Business Science, Gran Colombia University, Bogota, Colombia
| [b] Department of Industrial Engineering, Andes University, Bogota, Colombia
| [c] Department of Statistics and Operations Research, Complutense University, Madrid, Spain
Correspondence:
[*]
Corresponding author. Fabian Castiblanco, Faculty of Business Science, Gran Colombia University, Bogota,
Colombia. E-mail: fabianalberto.castiblanco@ugc.edu.co.
Abstract: This paper proposes a couple of criteria for evaluating the quality and relevance of a fuzzy partition. These criteria are established from a fuzzy classification system and its recursive De Morgan triplet. We propose a comparison process between the classes of a fuzzy partition, based on a translation invariant similarity relation. Therefore a classification process is carried out with the equivalence relations determined by the similarity relation. Such a relation is built on the commutative group structure formed by the elements of the fuzzy classification system. Our approach is illustrated through an example on image analysis by the fuzzy c-means algorithm.
