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Article type: Research Article
Authors: Castiblanco, Fabiana; * | Franco, Camilob | Rodríguez, J. Tinguaroc | Montero, Javierc
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: [email protected].
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.
Keywords: Relevance, fuzzy classification system, translation invariant similarity relation, fuzzy partitions, proximity relations
DOI: 10.3233/JIFS-200286
Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 4211-4226, 2020
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