Association measures on [0,1]

Issue title: Dedicated to Professor Lotfi A. Zadeh and Fifty Years of Fuzzy Logic

Article type: Research Article

Authors: Batyrshin, Ildar Z.^*

Affiliations: Centro de Investigación en Computación (CIC), Instituto Politécnico Nacional, Mexico, Av. Juan de Dios Bátiz, Esq. Miguel Othón de Mendizábal S/N, Nueva Industrial Vallejo, Gustavo A. Madero, Ciudad de México, D.F., Mexico

Correspondence: [*] Corresponding author. Ildar Z. Batyrshin, Centro de Investigación en Computación (CIC), Instituto Politécnico Nacional, Mexico, Av. Juan de Dios Bátiz, Esq. Miguel Othón de Mendizábal S/N, Nueva Industrial Vallejo, Gustavo A. Madero, Ciudad de México, D.F., Mexico.batyr1@gmail.com

Abstract: The paper studies the functions defined on [0,1] by axioms similar to the properties of the correlation coefficient. The methods of generation of such functions by means of strong negations, similarity measures and pseudo-difference operations associated to t-conorms are proposed. The considered non-statistical association measures can be used in definition of association (or correlation) measures of fuzzy sets, in measuring associations in fuzzy inference and probabilistic reasoning.

Keywords: Association measure, correlation, t-conorm, similarity measure, strong negation, fuzzy logic, pseudo-difference, involution

DOI: 10.3233/IFS-151714

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 3, pp. 1011-1020, 2015