Generalizated local divergence measures

Article type: Research Article

Authors: Kobza, Vladimír^a | Janiš, Vladimír^a | Montes, Susana^{b; *}

Affiliations: [a] Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovakia | [b] Department of Statistics and Operational Research, University of Oviedo, Spain

Correspondence: [*] Corresponding author. Susana Montes, Department of Statistics and Operational Research, University of Oviedo, Spain. Tel.: +34 985182133; Fax: +34 985181902; E-mail: montes@uniovi.es.

Abstract: The comparison of sets is an important topic with application in several fields. Divergence measures were introduced as an adequate measure of comparison of two fuzzy sets and an alternative of the dissimilarities. The particular study for local divergences is here generalized to any t-conorm instead just the sum. The concept of divergence is revisited and studied in detail. This study is complemented with the whole characterization of a new family of divergence measures, the generalized local divergence measures. Some applications of these divergences in pattern recognition and decision making illustrate their utility.

Keywords: Divergence measure, T-conorm, locality, S-locality, aggregation operator

DOI: 10.3233/JIFS-161647

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 337-350, 2017