New Approaches For Fuzzy Classification And Their Applications

Fuzzy set theory (FST) plays an important role in dealing with imprecise, and uncertain information. It relaxes the precise number and exact relation constraints of classical set theory, by introducing fuzziness to the relation between the data. Fuzzy sets provide a wider and more flexible framework for dealing with data than traditional machine learning methods (e.g. neural networks, clustering methods, etc). FST is a mature research area, and has also been widely applied in the areas of mechanical control, pattern recognition, and decision support systems. Fuzzy-rough sets (a hybridisation of rough and fuzzy sets) and fuzzy neural networks (a hybridi-sation of neural networks and fuzzy sets) have enjoyed much attention as two fuzzy set theory based approaches.Rough set theory was also proposed as a mathematical tool for dealing with imperfect and incomplete knowledge. Compared with FST, rough set theory is more concerned with a dif-ferent type of uncertainty:indiscernibility. However,due to its definition, rough sets can only operate effectively with datasets containing discrete values. By employing a fuzzy equivalence relation and fuzzy logical operators instead of a crisp equivalence relation and classical logical operators,respectively, fuzzy-rough sets provide a means by which the relationship between dis-crete data or real-valued data (or a mixture of both) can be effectively analysed. In this thesis, fuzzy-rough nearest-neighbour classification algorithms are studied from both methodological and theoretical perspectives. From theoretical development, a kernel-based fuzzy-rough set tech-nique and associated nearest-neighbour algorithms are proposed. Real-world medical datasets for the task of mammographic risk assessment are employed in order to evaluate such classi-fication approaches. The experimental results demonstrate that such kernel-based fuzzy-rough nearest-neighbour approaches offer improved and more robust performances over other classi-fiers. Theoretically, the underlying mechanism of fuzzy-rough nearest-neighbour (FRNN) and vaguely quantified nearest-neighbour (VQNN) algorithms are explored. The research shows that the resulting classification of FRNN and VQNN depends only upon the highest similarity and greatest summation of the similarities of each class, respectively. This fact is exploited in or-der to formulate two novel fuzzy similarity-based parallel methods. Furthermore, a generalised fuzzy similarity-based nearest-neighbour framework is presented. The theoretical proof and em-pirical evaluation demonstrate that FRNN and VQNN can be considered as the special cases of the proposed new framework. As the combination of fuzzy systems with neural networks, fuzzy neural networks have two main categories:1) The fuzzified structure of neural networks are implemented via introducing the fuzzy sets to neural networks. In so doing, the range and the ability of processing information for neural networks can be widened and improved.2) The fuzzy information is handled under the framework of neural networks. By using the training algorithms for neural networks, the fuzzy rules and the fuzzification approaches can be automatically extracted and optimised from both constructive and methodological perspectives. In this thesis, the hybridisation of the zero-order TSK fuzzy system with the evolutionary extreme learning machine approach leads an evolutionary fuzzy extreme learning machine. This technique is also applied to the task of mammographic risk analysis. The experimental results demonstrate that the evolutionary fuzzy extreme learning machine offers improved classification accuracy, both at the overall image level and at the level of individual risk types. Also, a local coupled feed-forward neural network is also used as the property for fuzzification for this work. In order to enhance the lcarning efficiency, a modified gradient-based learning method is employed to train such neural networks. The monotonicity of the error functions and the weak and strong convergence results for this algorithm are also proven.