Metodología para el Diseño de Conjuntos Difusos Tipo-2 a partir de Opiniones de Expertos

Context: There is a need for processing information coming from human like language thatincludes uncertainty in order to solve problems defined in that context.Method: We use Type-2 fuzzy sets for defining and measuring human like language, so wepropose a methodology for designing them. The proposal is composed by three key steps:(1) defining a linguistic label (word), (2) defining its membership function, and (3) collectinginformation from experts.Results: The proposal is applied and validated in a real scenario based on triangular fuzzysets through two different groups of experts. We present a proposal to model, process andanalyze input information coming from experts that allows to do an appropriate handling ofuncertainty present in people perceptions.Conclusions: The proposed methodology is applicable to different problems where differentpeople express their opinions and/or perceptions about a specific problem.ResumenContexto: Existe una creciente necesidad de procesar la información proveniente del lenguaje humano, la cual incluye incertidumbre, con el fin solucionar problemas definidos en un determinado contexto.Método: Empleamos conjuntos difusos Tipo-2 a fin de representar y cuantificar el lenguaje humano, para lo cual presentamos una serie de aspectos metodológicos para su diseño. La propuesta se compone de tres actividades clave: (1) determinar la etiqueta lingüística (palabra), (2) definir su función de pertenencia y (3) recolectar la información desde los expertos.Resultados: Se aplica y valida la propuesta en un escenario real basado en conjuntos triangulares a través de la comparación de dos grupos de expertos. Se modela, procesa y analiza la información de entrada permitiendo hacer un manejo adecuado a la incertidumbre implícita en sus opiniones.Conclusiones: La metodología propuesta es aplicable a diferentes situaciones, donde múltiples sujetos expresan su opinión o percepción que manifiestan alrededor de determinado problema.

Geometric Fuzzy Logic Systems

There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems