A proposed fuzzy system modeling algorithm with an application in pharmacokinetic modeling

In this thesis, a new fuzzy system modeling algorithm is proposed to address some of the limitations of existing approaches. The new algorithm differs from existing ones in its approach to (i) input membership assignment; a new n-dimensional rule structure is proposed which does not assume an a priori shape for the fuzzy clusters and does not break the natural ties among the data vector; (ii) significant input determination; a fuzzy supervised learning approach is developed which assigns a significance degree to the input variables unlike the existing algorithms that classifies an input variable as either significant or not; (iii) degree of firing determination and inference; a k-NN based approach is developed since the existing algorithms are not applicable to the new n-dimensional antecedent structure proposed; (iv) fuzzy output clustering; problems with the well-known and widely referred FCM [3] algorithm are revealed and a new clustering algorithm is proposed. Furthermore, a Type 2 fuzzy system modeling, which is, based on interval-valued membership degrees rather than singleton membership degrees (as is with Type 1 modeling) is provided.; The proposed algorithms (Type 1 and Type 2) are evaluated in terms of predictive performance and determination of the significance degrees in two different data sets and compared with other algorithms that exist in the literature. The first data set is a two-input single output nonlinear function prediction, which is used as benchmark in the literature. The second data set is from the clinical pharmacology field, namely pharmacokinetic modeling of lithium. The proposed algorithms are compared with different pharmacokinetic modeling approaches from the literature. The comparisons demonstrated that the proposed algorithms could be successfully applied in pharmacokinetic modeling.; Overall results showed that the proposed fuzzy system modeling could effectively approximate nonlinear functions with simple fuzzy if-then rules, which does not assume a priori structure for the model. This is compatible with other recent research that demonstrates that fuzzy system modeling algorithms are universal approximaters.; A theoretical result, which shows that the fuzzy containment property does not hold for continuous nonarchemedean De Morgan triples, is also included in the thesis.