Wolkenhauer O. Data Engineering. Fuzzy Mathematics in Systems Theory and Data Analysis

John Wiley, 2001. — 288.Textbooks on fuzzy systems, system theory, time-series and data analysis traditionally describe a theoretical framework or particular methodology and then apply these concepts to problems. I believe that such a strategy is not optimal, nor docs it seems adequate to deal with the current challenges in science and engineering. Researchers in system and control theory have, over the last few decades, "zoomed in" on certain aspects of the theory, refined their mathematical tools to tremendous depths, and at the same time established various schools of thought. The subsequent accumulation of a vast amount of theoretical material within any particular area has condemned young researchers to specialize in a particular technique whereby they tend to lose the 'big picture'. Such overspecialization in training often makes it more difficult to choose an adequate framework within which to work. I contend that starting from the problem at hand, with the available information and an understanding of the uncertainty involved, we require knowledge of mOre than one methodology and how the different theoretical frameworks can be related. We shall therefore start in this book with system models and the information available to build them. Uncertainty is considered by formalizing the intuitive concept of 'expectation’, from which we subsequently derive quantitative measures of uncertainty (statistics, fuzzy measures). Fuzzy sets and fuzzy relations will emerge 'naturally' from considering the application of theories (models) to observations (data). To relate formal models to sampled data, we have to generalize set-operations (as the basis for comparisons) and transitivity (as the basis for reasoning).
This book introduces fuzzy systems sympathetically explaining its philosophical implications and practical applications. There are four main themes or arguments running through the book: reformulating systems theory to take account of fuzzy systems and possihility theory; introducing data engineering as the discipline, which for a given set of complex, uncertain data, extracts information by detecting pattern, and thereby turns information into the evidence used in decision making (classification, prediction and control); the quest for a mcthodology which enables us to combine quantitative formal analysis with qualitative context-dependent expert. Knowledge; that when solving a real-world problem, (matching observations with a model) an empirical approach (implying heuristics) is perfectly acceptable.System Analysis
Uncertainty Techniques
Learning from Data: System Identification
Propositions as Subsets of the Data Space
Fuzzy Systems and Identification
Random-Set Modeling and Identification
Certain Uncertainty
Fuzzy Inference Engines
Fuzzy Classification
Fuzzy Control
Fuzzy Mathematics