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.
