key features
systems science
authors
analysis
Klir
problem
monograph
books
concept
Binghamton University
name
features
Choquet integral
levels
paper
Wang
integrals
extensive bibliography
theory
new concept
data mining
bibliography
exposition
original results
important new results
University
interest
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final chapter
2009-01-01
additivity
method
types
Department
seminars
nonlinear integrals
text
false
graduate level
2009
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classroom
Omaha
mathematical analysis
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2022-01-01T19:05
index
upper integral
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.
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Thomas J. Watson School of Engineering, Department of Systems Science &, Binghamton University, 13902, Binghamton, U.S.A.
Thomas J. Watson School of Engineering, Department of Systems Science &, Binghamton University, 13902, Binghamton, U.S.A.
Wang
Zhenyuan
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Klir
George J.
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Springer Nature - SN SciGraph project
Springer Nature
Department of Mathematics, University of Nebraska at Omaha, Dodge St. 6001, 68182, Omaha, U.S.A.
Department of Mathematics, University of Nebraska at Omaha, Dodge St. 6001, 68182, Omaha, U.S.A.
Mathematical Sciences