Centroid of an Interval Type-2 Fuzzy Set: Continuous vs. Discrete

• Main Authors: Omar Salazar Morales, José Humberto Serrano Devia, José Jairo Soriano Mendez
• Format: Article
• Language: Spanish
• Published: Universidad Distrital Francisco José de Caldas 2011-12-01
• Series: Ingeniería
• Subjects: Centroid, Karnik-Mendel algorithm, interval type-2 fuzzy set, recursive algorithm.
• Online Access: http://revistas.udistrital.edu.co/ojs/index.php/reving/article/view/3834

Karnik-Mendel algorithm involves execution of two independent procedures for computing the centroid of an interval type-2 fuzzy set: the first one for computing the left endpoint of the interval centroid (which is denoted by cl), and the second one for computing its right counterpart (which is denoted by cr). Convergence of the discrete version of the algorithm to compute the centroid is known, whereas convergence of the continuous version may exhibit some issues. This paper shows that the calculation of cl and cr are really the same problem on the discrete version, and also we describe some problems related with the convergence of the centroid on its continuous version.