This monograph is an attempt to unify existing works in the field
of random sets, random variables, and linguistic random variables
with respect to statistical analysis. It is intended to be a
tutorial research compendium. The material of the work is mainly
based on the postdoctoral thesis (Ha- bilitationsschrift) of the
first author and on several papers recently published by both
authors. The methods form the basis of a user-friendly software
tool which supports the statistical inferenee in the presence of
vague data. Parts of the manuscript have been used in courses for
graduate level students of mathematics and eomputer scienees held
by the first author at the Technical University of Braunschweig.
The textbook is designed for readers with an advanced knowledge of
mathematics. The idea of writing this book came from Professor Dr.
H. Skala. Several of our students have significantly contributed to
its preparation. We would like to express our gratitude to Reinhard
Elsner for his support in typesetting the book, Jorg Gebhardt and
Jorg Knop for preparing the drawings, Michael Eike and Jiirgen
Freckmann for implementing the programming system and Giinter
Lehmann and Winfried Boer for proofreading the manuscript. This
work was partially supported by the Fraunhofer-Gesellschaft. We are
indebted to D. Reidel Publishing Company for making the pub-
lication of this book possible and would especially like to
acknowledge the support whieh we received from our families on this
project.
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