The issue of second-order uncertainty has received relatively little attention so far, but its intrinsic importance is certain to make it an object of growing attention in coming years. Through their work, the authors have opened a door to wide-ranging applications. They deserve our compliments and congratulations. Berkeley, CA November 30, 2008 Lotfi A. Zadeh
XIV PrefaceAfter testing the new fuzzy functions tools on various benchmark problems, the algorithms are successfully applied to model decision processes in two real problem domains: the desulphurization process in steel making and stock price prediction activities. For both of these problems, the proposed methods produce robust and high performance results, which are comparable (if not better) than the best system modeling approaches known in the current literature. Several aspects of the proposed methodologies are thoroughly analyzed to provide a deeper understanding. These analyses show consistency of the results.As a final note, the fuzzy modeling approaches demonstrated in this book may supply suitable framework for engineers, and practitioners for a design of complex systems with fuzzy functions instead of crisp functions, that is to say, for a design of artificial systems based on well known functions, viz. regression, classification, etc. Although in this book we only show examples from economy and production industry, we believe that fuzzy modeling can and should be utilized in many fields of science, including biology, economics, psychology, sociology, history and more. In such fields, many models exist in current research literature and they can be directly transformed into mathematical models using the methodologies presented herein.