Extending the Concepts of Type-2 Fuzzy Logic and Systems
Metadatos
Mostrar el registro completo del ítemAutor
Ruiz García, GonzaloEditorial
Universidad de Granada
Departamento
Universidad de Granada. Programa Oficial de Doctorado en Tecnologías de la Información y la ComunicaciónMateria
Teoría de Conjuntos Lógica difusa Sistemas difusos Análisis de sistemas Optimización matemática
Materia UDC
654 655 316.77 3325
Fecha
2017Fecha lectura
2017-09-14Referencia bibliográfica
Ruiz García, G. Extending the Concepts of Type-2 Fuzzy Logic and Systems. Granada: Universidad de Granada, 2017. [http://hdl.handle.net/10481/48265]
Patrocinador
Tesis Univ. Granada. Programa Oficial de Doctorado en Tecnologías de la Información y la ComunicaciónResumen
The work presented in this dissertation is a contribution to the
field of fuzzy sets and fuzzy logic systems theory.
Firstly, we will approach the controversial discussion that has
been effusively debated among scholars of fuzzy logic for many
years. Some authors argue that the ability of type-2 fuzzy logic
systems to perform better than their type-1 counterparts relies
on the higher number of parameters they need to be defined. On
the other hand, other authors pose the argument that this ability
is due to how those parameters are used, and how type-2 fuzzy
sets model uncertainty in a more suitable way. Although other
previous works have tackled this discussion, we propose a new
approach based on a function approximation framework, using
type-1 fuzzy logic systems with a varying number of parameters.
This part of the work aims to support the previous findings
related to this topic, and justify the further research on type-2
fuzzy sets and fuzzy logic systems in the rest of the dissertation.
Secondly, after shedding some light on the previous discussion,
we will focus on the development of the theory about type-
2 fuzzy sets and fuzzy logic systems. Traditionally, although
type-2 fuzzy logic has proven to perform better than type-1, its
use has been somehow limited. One of those reasons has been
the limitation to operate with those sets; although the operations
of intersection and union on these sets were defined at
the same time that type-2 fuzzy sets themselves, the operations
were computationally intensive, and closed formulas were only
available for type-2 fuzzy sets having normal and convex secondary
grades. The main contribution of this work to the fuzzy
sets theory is to provide two new theorems for the intersection
and union operations, regardless of the specific shape of the sets’
secondary grades.
Those new theorems, which allow us to operate on type-2
fuzzy sets having non-convex secondary grades, are the keystone
to further developing the theory of interval type-2 fuzzy logic
systems. Interval type-2 fuzzy sets have been recently shown to
be more general than interval-valued fuzzy sets, and can actually
have non-convex secondary grades. Hence, a whole new theory
needs to be developed in order to provide those fuzzy logic systems
with the appropriate theoretical framework; we aim to do
so in the last part of this dissertation.