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Introduction

  • Zhenyuan Wang
  • George J. Klir
Chapter
Part of the IFSR International Series on Systems Science and Engineering book series (IFSR, volume 25)

Generalized measure theory, which is the subject of this book, emerged from the well-established classicalmeasure theory by the process of generalization. As is well known, classical measures are nonnegative real-valued set functions, each defined on a specific class of subsets of a given universal set, that satisfy certain axiomatic requirements. One of these requirements, crucial to classical measures, is known as the requirement of additivity. This requirement is basically that the measure of the union (finite or countably infinite) of any recognized family of sets that are pairwise disjoint be equal to the sum of measures of the individual sets in the union. In generalized measure theory, the additivity requirement is replaced with a considerably weaker requirement. Any real-valued set function \(\\mu\)

Keywords

Fuzzy Measure Classical Measure Possibility Measure Imprecise Probability Classical Probability Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Nebraska at OmahaOmahaU.S.A
  2. 2.Department of Systems Science and Industrial EngineeringThomas J. Watson School of Engineering and Applied Sciences Binghamton UniversityBinghamtonU.S.A

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