Uncertainty is an inherent part of real-world applications. The use of new methods for handling uncertainty has fundamental importance in modeling complex systems from various domains of activity. The present book has as goal the representation and utilization of uncertainty by means of fuzzy functions.
The book begins with a very good overview of the basic notions and principles related to fuzzy sets and systems: type-1 fuzzy sets, fuzzy logic, fuzzy relations, type-2 fuzzy sets, fuzzy inference systems. Another chapter is dedicated to fuzzy clustering. It starts with some fuzzy clustering algorithms (C-means, C-regression, combined fuzzy clustering algorithm). Then, a new improved fuzzy clustering algorithm is proposed to be used for a new fuzzy modeling approach, named “improved fuzzy functions” and its extension for classification models is presented. Two new cluster validity indices are introduced in order to identify the optimum number of clusters. In order to demonstrate the performance of these new indices three simulation experiments finish this chapter.
The next chapter presents a mathematical theory for “fuzzy functions” and “improved fuzzy functions” and their applications to build fuzzy models for regression and classification problems using type-1 fuzzy sets. Also, evolutionary type-1 improved fuzzy function systems are analyzed. For all systems, the structure identification and the inference mechanism are presented.
Chapter 5 studies fuzzy models based on type-2 fuzzy sets: conventional type-2 fuzzy systems, discrete interval type-2 improved fuzzy function systems, discrete interval type-2 improved fuzzy functions with evolutionary algorithms. The uncertainties are captured by automatic identification of the structure of fuzzy functions.
The next chapter presents various experiments to evaluate the performance of the proposed algorithms. These experiments demonstrate the effectiveness of the proposed approach against other approaches.
The fuzzy models proposed in this book can be used with success by researchers from various domains of activity: engineering, economics, biology, sociology etc., in order to model complex systems.