—This paper presents a novel approach to the representation of type-1 and type-2 fuzzy sets utilising computational geometry. To achieve this our approach borrows ideas from the field of computational geometry and applies these techniques in the novel setting of fuzzy logic. We provide new algorithms for various operations on type-1 and type-2 fuzzy sets… (More)
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract—Construction of interval type-2 fuzzy set models is the first step in the Perceptual Computer, an implementation of Computing with Words. The Interval Approach (IA) has been so far the only… (More)
— This paper presents the geometric defuzzifier for generalised type-2 fuzzy sets. This defuzzifier can be executed in real-time and can therefore be applied to control and other real world problems. We believe this to be a significant step forward for generalised type-2 fuzzy logic systems.
Defuzzification of type-2 fuzzy sets is a com-putationally intense problem. This paper proposes a new approach for defuzzification of interval type-2 fuzzy sets. The collapsing method converts an interval type-2 fuzzy set into a representative embedded set (RES) which, being a type-1 set, can then be de-fuzzified straightforwardly. The novel Representative… (More)
For generalised type-2 fuzzy sets the defuzzification process has historically been slow and inefficient. This has hampered the development of type-2 Fuzzy Inferencing Systems for real applications and therefore no advantage has been taken of the ability of type-2 fuzzy sets to model higher levels of uncertainty. The research reported here provides a novel… (More)
— In this paper we evolve the parameters of a proportional, integral, and derivative (PID) controller for an unstable, complex and nonlinear system. The individuals of the applied genetic algorithm (GA) are evaluated on the actual system rather than on a simulation of it. This makes implicit a formal model identification for the implementation of a… (More)