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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.
List of contents
Mathematical Representation of Simple Data and Connections.- Specification and Use of Observation Fuzziness.- Specification and Use of Uncertain Variability.- Specification of Vagueness of Statements on Sets.- Methods from Qualitative Data Analysis.- Evaluation of Functional Relationships.- Outlook and Conclusions.
Summary
"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.
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From the reviews
"This monograph is an English translation of the German original from 1997 … . The book is intended to assist practitioners to successfully use mathematical resources when dealing with uncertainty. … the ideas presented in this book remain valid and helpful especially for practitioners in helping them to decide for an appropriate software tool when dealing with data suffering from uncertainty." (Radko Mesiar, Zentralblatt MATH, Vol. 1084, 2006)
"This book is about mathematical modeling and analysis of uncertainty in real-world problems. … The book is recommended for all who deal with complex data, especially in the social sciences and intelligence technology." (Hung Trung Nguyen, Mathematical Reviews, Issue 2007 b)
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From the reviews
"This monograph is an English translation of the German original from 1997 ... . The book is intended to assist practitioners to successfully use mathematical resources when dealing with uncertainty. ... the ideas presented in this book remain valid and helpful especially for practitioners in helping them to decide for an appropriate software tool when dealing with data suffering from uncertainty." (Radko Mesiar, Zentralblatt MATH, Vol. 1084, 2006)
"This book is about mathematical modeling and analysis of uncertainty in real-world problems. ... The book is recommended for all who deal with complex data, especially in the social sciences and intelligence technology." (Hung Trung Nguyen, Mathematical Reviews, Issue 2007 b)
