Estudio teórico y experimental de métodos de defusificación de conjuntos difusos tipo dos de intervalo

Abstract

In this monograph is carried out a theoretical and experimental study of Karnik-Mendel type defuzzification methods of interval type-2 fuzzy sets, using sets with continuous domain. The algorithms studied correspond to: Enhanced Karnik Mendel (EKM), Enhanced Iterative Algorithm with Stop Condition (EIASC), IASC2, KM2 and Enhanced Opposite Direction Searching (EODS). New algorithms are proposed as result of the application of root finding methods: Bisection, Halley and exhaustive search. Second-order polynomials are proposed, whose roots are used as starting points for the algorithms. The experimental study consists of an ANOVA analysis, followed by the TUKEY HSD test. The main theoretical results are: Show that the EODS is not a KM type algorithm, identify the disadvantages of the IASC2 and KM2 algorithms against EIASC and EKM. The main experimental results are: A new exhaustive search algorithm alternative to the EIASC; two new alternative algorithms to the EKM, one of them resulting from the application of the Newton-Raphson method and another one from the Halley method. In both cases, using the root of a second-order polynomial as the starting point.