New measures of similarity based on fuzzy implications

Article type: Research Article

Authors: González-Caballero, Erick^a | Díaz, Susana^b | Espín, Rafael^c | Montes, Susana^{b; *}

Affiliations: [a] Higher Polytechnic Institute of Havana, Cuba | [b] Department of Statistics and Operational Research, University of Oviedo, Spain | [c] Autonomous University of Coahuila, Mexico

Correspondence: [*] Corresponding author. Susana Montes, Department of Statistics and Operational Research, University of Oviedo, Spain. E-mail: montes@uniovi.es.

Abstract: An important problem in fuzzy theory is how to determine if two elements are similar or not. There are different definitions to measure how similar or close are elements. One of the most important concepts in this context is that one of similarity. This paper aims at studying fuzzy similarities defined by fuzzy implications, logical equivalences expressed by fuzzy bi-implication operators and aggregation operators. We propose a definition of proximity between two fuzzy finite sets by using the previous operators and we study when this type of operators satisfy the formal definition of similarity.

Keywords: Similarity measure, fuzzy set, logical equivalence, fuzzy implication

DOI: 10.3233/JIFS-16861

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3493-3503, 2017