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Mathematics of Uncertainty: Ideas, Methods, Application Problems

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"Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships. The notions of randomness and probability are examined as a model for the variability of observation and measurement results. Besides these basic ideas the book also presents methods of qualitative data analysis such as cluster analysis and classification, and of evaluation of functional relationships such as regression analysis and quantitative fuzzy data analysis.

The aim of the book did not require any remarkable changes with respect to contents and presentation for a translation of the German version. Only the references to textbooks in German language were omitted, as a rule, in the translation.

Since this preface is followed by the translation of the foreword to the German edition, which contains also remarks on intention and organization of the present book, it may suffice here to restrict oneself to appreciate all the support the author received in preparation and in writing the present translation.

The author has to thank his former colleagues from the Technical University Bergakademie Freiberg, Professor Dietrich Stoyan, particularly for his critical examination of the German version and his valuable remarks and suggestions, Professor Wolfgang N¨ather, particularly for his hints to recent publications and his constant readiness for discussion and support, finally, Ingenieur of informatics Irmgard Gugel, for her again excellent work of final technical edition and completion of the manuscript. Moreover, the author acknowledges with thanks the encouragement and occasional support by Professor Reinhard Viertl, Wien, and hints to recent publications by Professor J¨urgen Pilz, Klagenfurt.

The author is indebted to Springer-Verlag Heidelberg, represented by Dr. Thomas Ditzinger, for having included the title in the list of his famous Publishing House.

Finally, the author thanks again his wife for her permanent encouragement and understanding consideration, which made the completion also of this translation possible.

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