Musikasuwan, Salang
(2013)
Novel fuzzy techniques for modelling human decision making.
PhD thesis, University of Nottingham.
Abstract
Standard (type1) 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 type1 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 nonconvex membership functions in the context of human decision making systems were investigated. It was demonstrated that nonconvex 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. Type2 fuzzy sets feature membership functions that are themselves fuzzy sets. While type2 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 type2 fuzzy sets, Garibaldi previously proposed the term ‘nondeterministic 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 nonstationary fuzzy set. The concept of random perturbations that can be used for generating these nonstationary 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 nonstationary fuzzy sets (this is similar to the footprint of uncertainty of type2 sets). Basic operators, i.e. union, intersection and complement, for nonstationary fuzzy sets are also proposed. Proofs of properties of nonstationary fuzzy sets to satisfy the set theoretic laws are also given in this thesis.
It can be observed that, firstly, a nonstationary fuzzy set is a collection of type1 fuzzy sets in which there is an explicit, defined, relationship between the fuzzy sets. Specifically, each of the instantiations (individual type1 sets) is derived by a perturbation of (making a small change to) a single underlying membership function. Secondly, a nonstationary fuzzy set does not have secondary membership functions, and secondary membership grades. Hence, there is no ‘direct’ equivalent to the embedded type2 sets of a type2 fuzzy sets. Lastly, the nonstationary inference process is quite different from type2 inference, in that nonstationary inference is just a repeated type1 inference.
Several case studies have been carried out in this research. Experiments have been carried out to investigate the use of nonstationary fuzzy sets, and the relationship between nonstationary and interval type2 fuzzy sets. The results from these experiments are compared with results produced by type2 fuzzy systems. As an aside, experiments were carried out to investigate the effect of the number of tunable parameters on performance in type1 and type2 fuzzy systems. It was demonstrated that more tunable parameters can improve the performance of a nonsingleton type1 fuzzy system to be as good as or better than the equivalent type2 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.
Item Type: 
Thesis (University of Nottingham only)
(PhD)

Supervisors: 
Garibaldi, J.M. 
Keywords: 
NonStationary Fuzzy Set, Type2 Fuzzy Set, Human Decision Making 
Subjects: 
Q Science > QA Mathematics 
Faculties/Schools: 
UK Campuses > Faculty of Science > School of Computer Science 
Item ID: 
13161 
Depositing User: 
EP, Services

Date Deposited: 
06 Nov 2013 10:57 
Last Modified: 
13 Sep 2016 21:46 
URI: 
http://eprints.nottingham.ac.uk/id/eprint/13161 
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