Statistical methods for fuzzy data Statistical Methods forFuzzy Data; Contents; Preface; Part I FUZZY INFORMATION; 1 Fuzzy data; 1.1 One dimensional fuzzy data; 1.2 Vector valued fuzzy data; 1.3 Fuzziness and variability; 1.4 Fuzziness and errors; 1.5 Problems; 2 Fuzzy numbers and fuzzy vectors; 2.1 Fuzzy numbers and characterizing functions; 2.2 Vectors of fuzzy numbers and fuzzy vectors; 2.3 Triangular norms; 2.4 Problems; 3 Mathematical operations for fuzzy quantities; 3.1 Functions of fuzzy variables; 3.2 Addition of fuzzy numbers; 3.3 Multiplication of fuzzy numbers; 3.4 Mean value of fuzzy numbers. Statistical data are not always precise numbers or vectors or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data environmental biological medical sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book the foundations of the description of fuzzy data are explained including methods on how to obtain the characterizing function of fuzzy m