Note publique d'information : This comprehensive text examines the relatively new mathematical area of generalized
measure theory. This area expands classical measure theory by abandoning the requirement
of additivity and replacing it with various weaker requirements. Each of these weaker
requirements characterizes a class of nonadditive measures. This results in new concepts
and methods that allow us to deal with many problems in a more realistic way. For
example, it allows us to work with imprecise probabilities. The exposition of generalized
measure theory unfolds systematically. It begins with preliminaries and new concepts,
followed by a detailed treatment of important new results regarding various types
of nonadditive measures and the associated integration theory. The latter involves
several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and
lower and upper integrals. All of the topics are motivated by numerous examples, culminating
in a final chapter on applications of generalized measure theory. Some key features
of the book include: many exercises at the end of each chapter along with relevant
historical and bibliographical notes, an extensive bibliography, and name and subject
indices. The work is suitable for a classroom setting at the graduate level in courses
or seminars in applied mathematics, computer science, engineering, and some areas
of science. A sound background in mathematical analysis is required. Since the book
contains many original results by the authors, it will also appeal to researchers
working in the emerging area of generalized measure theory. About the Authors: Zhenyuan
Wang is currently a Professor in the Department of Mathematics of University of Nebraska
at Omaha. His research interests have been in the areas of nonadditive measures, nonlinear
integrals, probability and statistics, and data mining. He has published one book
and many papers in these areas. George J. Klir is currently a Distinguished Professor
of Systems Science at Binghamton University (SUNY at Binghamton). He has published
29 books and well over 300 papers in a wide range of areas. His current research interests
are primarily in the areas of fuzzy systems, soft computing, and generalized information
theory.