1 Introduction.- 2 Vague Data.- 3 Fuzzy Sets of the Real Line.- 4 Operations on Fuzzy Sets.- 4.1 Set Theoretical Operations.- 4.2 On Zadeh's Extension Principle.- 4.3 Arithmetic Operations.- 5 Representation of Vague Data in a Digital Computer.- 6 Topological Properties of Fuzzy Set Spaces.- 7 Random Sets and Fuzzy Random Variables.- 8 Descriptive Statistics with Vague Data.- 8.1 Expected Value.- 8.2 Variance.- 8.3 Empirical Distribution Function.- 9 Distribution Functions and i.i.d.-Sequences of Random Variables.- 10 Limit Theorems.- 10.1 Strong Law of Large Numbers.- 10.2 Consistent Estimators in the Finite Case.- 10.3 Gliwenko-Cantelli Theorem.- 10.4 Related Results.- 11 Some Aspects of Statistical Inference.- 11.1 Parametric Point Estimation.- 11.2 Confidence Estimation.- 11.3 The Testing of Hypotheses.- 12 On a Software Tool for Statistics with Vague Data.- 12.1 Linguistic Modelling.- 12.2 Linguistic Approximation.- 12.3 Examples.- References.- List of Symbols.

Autorentext

Dr. Rudolf Kruse is the former leader of the Computational Intelligence Research Group and now Emeritus Professor of the Department of Computer Science at the University of Magdeburg, Germany. Dr. Sanaz Mostaghim is a full Professor of Computer Science and Dr. Christian Braune is a Senior Lecturer at the same institution. Dr. Christian Borgelt is a Professor of Data Science at the Paris Lodron University of Salzburg, Austria. Dr. Matthias Steinbrecher is a Development Architect at SAP SE, Potsdam, Germany.