Improved uncertainty modeling and handling using type-2 fuzzy logic

Type-1 Fuzzy Logic (T1 FL) has been successfully applied in various engineering areas over the past 40 years. This fact can be attributed to the ability of T1 FL to cope with the linguistic uncertainty originating in the imprecise and vague meaning of words. However, when various kinds of data uncertainties are encountered, the performance of TI FL based systems can deteriorate. To address this issue, the concept of Type-2 (T2) FL was proposed by Lofti Zadeh in 1975 as an extension to T1 FL. The fundamental difference between T1 and T2 FL is in the model of individual Fuzzy Sets (FSs), where T2 FSs employ membership degrees that are themselves fuzzy. T2 FL has experienced a widespread of research interest in the past decade and it constitutes evolving and very active area of research. Some of the major challenges of the currently developed theory of T2 FL can be identified as follows: i) high computational complexity of T2 FL algorithms, ii) lack of established design methodology for creating robust T2 FL systems, and iii) lack of understanding of the uncertainty modeling capabilities of T2 FL systems.;This dissertation contributes by introducing novel enhanced algorithms and methodologies in the identified deficient areas of T2 FL. First, new algorithms for type-reduction of General T2 (GT2) FSs, the Monotone Centroid Flow algorithm and the Importance Sampling based defuzzification algorithm, are proposed, addressing the computationally most intensive stage of fuzzy inference with GT2 FL systems. Next, a novel simplified representation for GT2 FSs, the Shadowed T2 FSs is introduced combining the computational efficiency of Interval T2 (IT2) FSs with the rich uncertainty modeling capability of GT2 FSs. Further, new methodologies are proposed to analyze the robustness and input-output uncertainty modeling of IT2 FL systems. Finally, several novel applications of both IT2 as well as GT2 FL methods are developed. The IT2 FL was applied in the area of uncertain fuzzy voting. The GT2 FL was utilized in the development of the GT2 Fuzzy uncertain fuzzy clustering algorithms. The presented algorithms constitute first of a kind applications of T2 FL in the respective areas demonstrating the benefits of using 12 FL in scenarios with increased amount of uncertainty.