Novel fuzzy techniques for modelling human decision making

Standard (type-1) fuzzy sets were introduced to resemble human reasoning in its use of approximate information and uncertainty to generate decisions. Since knowledge can be expressed in a more natural by using fuzzy sets, many decision problems can be greatly simplified. However, standard type-1 fuzzy sets have limitations when it comes to modelling human decision making. In many applications involving the modelling of human decision making (expert systems) the more traditional membership functions do not provide a wide enough choice for the system developer. They are therefore missing an opportunity to produce simpler or better systems. The use of complex non-convex membership functions in the context of human decision making systems were investigated. It was demonstrated that non-convex membership functions are plausible, reasonable membership functions in the sense originally intended by Zadeh. All humans, including ‘experts’, exhibit variation in their decision making. To date, it has been an implicit assumption that expert systems, including fuzzy expert systems, should not exhibit such variation. Type-2 fuzzy sets feature membership functions that are themselves fuzzy sets. While type-2 fuzzy sets capture uncertainty by introducing a range of membership values associated with each value of the base variable, but they do not capture the notion of variability. To overcome this limitation of type-2 fuzzy sets, Garibaldi previously proposed the term ‘non-deterministic fuzzy reasoning’ in which variability is introduced into the membership functions of a fuzzy system through the use of random alterations to the parameters. In this thesis, this notion is extended and formalised through the introduction of a notion termed a non-stationary fuzzy set. The concept of random perturbations that can be used for generating these non-stationary fuzzy sets is proposed. The footprint of variation (FOV) is introduced to describe the area covering the range from the minimum to the maximum fuzzy sets which comprise the non-stationary fuzzy sets (this is similar to the footprint of uncertainty of type-2 sets). Basic operators, i.e. union, intersection and complement, for non-stationary fuzzy sets are also proposed. Proofs of properties of non-stationary fuzzy sets to satisfy the set theoretic laws are also given in this thesis. It can be observed that, firstly, a non-stationary fuzzy set is a collection of type-1 fuzzy sets in which there is an explicit, defined, relationship between the fuzzy sets. Specifically, each of the instantiations (individual type-1 sets) is derived by a perturbation of (making a small change to) a single underlying membership function. Secondly, a non-stationary fuzzy set does not have secondary membership functions, and secondary membership grades. Hence, there is no ‘direct’ equivalent to the embedded type-2 sets of a type-2 fuzzy sets. Lastly, the non-stationary inference process is quite different from type-2 inference, in that non-stationary inference is just a repeated type-1 inference. Several case studies have been carried out in this research. Experiments have been carried out to investigate the use of non-stationary fuzzy sets, and the relationship between non-stationary and interval type-2 fuzzy sets. The results from these experiments are compared with results produced by type-2 fuzzy systems. As an aside, experiments were carried out to investigate the effect of the number of tunable parameters on performance in type-1 and type-2 fuzzy systems. It was demonstrated that more tunable parameters can improve the performance of a non-singleton type-1 fuzzy system to be as good as or better than the equivalent type-2 fuzzy system. Taken as a whole, the techniques presented in this thesis represent a valuable addition to the tools available to a model designer for constructing fuzzy models of human decision making

A novel dual surface type-2 fuzzy logic controller for a micro robot

Over the last few years there has been an increasing interest in the area of type-2 fuzzy logic sets and systems in academic and industrial circles. Within robotic research the majority of type-2 fuzzy logic investigations has been centred on large autonomous mobile robots, where resource availability (memory and computing power) is not an issue. These large robots usually have a variation of a Unix operating system on board. This allows the implementation of complex fuzzy logic systems to control the motors. Specifically the implementation of interval and geometric type-2 fuzzy logic controllers is of interest as they are shown to outperform type-1 fuzzy logic controllers in uncertain environments. However when it comes to using micro robots it is not practical to use type-1 and type-2 fuzzy logic controllers, due to the lack of memory and the processor time needed to calculate a control output value. The choice of motor controller is usually either fixed pre-set values, a variable scaled value or a PID controller to generate wheel velocities. In this research novel ways of implementing type-1 and interval type-2 fuzzy logic controllers on micro robots with limited resources are investigated. The solution thatis being proposed is the use of pre-calculated 3D surfaces generated by an off-line Fuzzy Logic System covering the expected ranges of the input and output variables. The surfaces are then loaded into the memory of the micro robots and can be accessed by the motor controller. The aim of the research is to test if there is an advantage of using type-2 fuzzy logic controllers implemented as surfaces over type-1 and PID controllers on a micro robot with limited resources. Control surfaces were generated for both type-1 and average interval type-2 fuzzy logic controllers. Each control surface was then accessed using bilinear interpolation to provide the crisp output value that was used to control the motor. Previously when this method has been used a single surface was employed to hold the information. This thesis presents the novel approach of the dual surface type-2 fuzzy logic controller on micro robots. The lower and upper values that are averaged for the classic interval type-2 controller are generated as surfaces and installed on the micro robots. The advantage is that nuances and features of both the lower and upper surfaces are available to be exploited, rather than being lost due to the averaging process. Having conducted the experiments it is concluded that the best approach to controlling micro robots is to use fuzzy logic controllers over the classical PID controllers where ever possible. When fuzzy controllers are used then type-2 fuzzy controllers (dual or single surface) should be used over type-1 fuzzy controllers when applied as surfaces on micro robots. When a type-2 fuzzy controller is used then the novel dual surface type-2 fuzzy logic controller should be used over the classic average surface. The novel dual surface controller offers a dynamic, weighted, adaptive and superior response over all the other fuzzy controllers examined