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