Design Considerations of Time in Fuzzy Systems

Fuzzy theory is an interesting name for a method that has been highly effective in a wide variety of significant, real-world applications. A few examples make this readily apparent. As the result of a faulty design the method of computer-programmed trading, the biggest stock market crash in history was triggered by a small fraction of a percent change in the interest rate in a Western European country. A fuzzy theory ap proach would have weighed a number of relevant variables and the ranges of values for each of these variables. Another example, which is rather simple but pervasive, is that of an electronic thermostat that turns on heat or air conditioning at a specific temperature setting. In fact, actual comfort level involves other variables such as humidity and the location of the sun with respect to windows in a home, among others. Because of its great applied significance, fuzzy theory has generated widespread activity internationally. In fact, institutions devoted to research in this area have come into being. As the above examples suggest, Fuzzy Systems Theory is of fundamen tal importance for the analysis and design of a wide variety of dynamic systems. This clearly manifests the fundamental importance of time con siderations in the Fuzzy Systems design approach in dynamic systems. This textbook by Prof. Dr. Jernej Virant provides what is evidently a uniquely significant and comprehensive treatment of this subject on the international scene.

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This book is outstanding for several reasons: it observes the role of time in fuzzy proposition calculations, provides calculation error analysis for small density of inference processing and gives numerous examples of fuzzy sets and systems programming with time incorporated into a fuzzy inference machine based on MATLAB and Mathematica packages. Major contributions in the field so far have only dealt with the JK fuzzy flip-flop; however, in this book the author covers analysis and simulation of various memory devices such as Delay, Trigger, Set-Reset etc. Simulations of fuzzy memory modules built with given memory cells are also presented. Audience: Readers from undergraduate to postgraduate level can comprehend the material of the book as it does not require high-level mathematics, yet it covers the entire spectra of fuzzy sets and possibility logic as related to time.

Contenu
List of Figures. List of Tables. Preface. Acknowledgments. Part I: The Fundamentals of Fuzzy and Possibilistic Logic. 1. Fuzziness and its Measure. 2. Fuzzy Operations and Relations. 3. Fuzzy Functions. 4. Fuzzy Algorithms. 5. Process of Fuzzy Inference. 6. Possibilistic Logic. Part II: Fuzzy Temporal Logic. 7. Temporality of Propositions. 8. Fuzziness of Time. 9. Temporality in Fuzzy Inference Machines. 10. Graphs of Fuzzy Dates. Part III: Fuzzy Sets Computation, Representation and Simulation. 12. Matlab Simulations of Fuzzy Circuits. Part IV: Programs. Appendices. References. Index.