15. Monotone Measures: Belief, Plausibility, Probability, and Possibility

  1. Timothy J. Ross

Published Online: 27 DEC 2010

DOI: 10.1002/9781119994374.ch15

Fuzzy Logic with Engineering Applications, Third Edition

Fuzzy Logic with Engineering Applications, Third Edition

How to Cite

Ross, T. J. (2010) Monotone Measures: Belief, Plausibility, Probability, and Possibility, in Fuzzy Logic with Engineering Applications, Third Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119994374.ch15

Author Information

  1. University of New Mexico, USA

Publication History

  1. Published Online: 27 DEC 2010
  2. Published Print: 15 JAN 2010

ISBN Information

Print ISBN: 9780470743768

Online ISBN: 9781119994374

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Keywords:

  • belief measure;
  • fuzzy set;
  • monotone measure;
  • plausibility measure;
  • possibility measures;
  • probability measures

Summary

This chapter develops the relationships between probability theory and evidence theory; to a limited extent, it also shows the relationship between a possibility theory, founded on crisp sets, and a fuzzy set theory. All of these theories are related under an umbrella theory termed monotone measures; all of these theories have been used to characterize and model various forms of uncertainty. The chapter developes monotone measures as an overarching framework for the other theories used to characterize various forms of uncertainty. The development continues with specific forms of monotone measures such as belief, plausibility, possibility, and probability. The chapter illustrates a new method in developing possibility distributions from empirical data, and describes a special kind of relationship between a possibility distribution and a fuzzy set. It provides examples to illustrate the various theories.

Controlled Vocabulary Terms

fuzzy set theory; possibility theory; probability