Mathematics of Uncertainty: Ideas, Methods, Application Problems

✍ Scribed by Professor Dr. Hans-Walter Bandemer (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2006
• Tongue: English
• Leaves: 198
• Series: Studies in Fuzziness and Soft Computing 189
• Edition: 1
• Category: Library

✦ Synopsis

"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.

✦ Table of Contents

Introduction....Pages 1-9
Mathematical Representation of Simple Data and Connections....Pages 11-38
Specification and Use of Observation Fuzziness....Pages 39-61
Specification and Use of Uncertain Variability....Pages 63-95
Specification of Vagueness of Statements on Sets....Pages 97-111
Methods from Qualitative Data Analysis....Pages 113-140
Evaluation of Functional Relationships....Pages 141-172
Outlook and Conclusions....Pages 173-176

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Probability Theory and Stochastic Processes; Applications of Mathematics; Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences; Artificial Intelligence (