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A Dual Measure of Uncertainty: The Deng Extropy.

Francesco Buono1, Maria Longobardi2

  • 1Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Università degli Studi di Napoli Federico II, I-80126 Naples, Italy.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary

We introduce Deng extropy, the dual of Deng entropy in evidence theory. This new measure is analyzed for its properties and applied to pattern recognition, showing its relevance.

Keywords:
Deng entropyextropypattern recognitionthe Dempster–Shafer evidence theory

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Area of Science:

  • Information Theory
  • Uncertainty Quantification
  • Dempster-Shafer Theory

Background:

  • Extropy is the dual concept of entropy.
  • Deng entropy is a measure of discrimination within Dempster-Shafer evidence theory.

Purpose of the Study:

  • Define Deng extropy as the dual of Deng entropy.
  • Analyze the relationship and behavior of Deng extropy.
  • Demonstrate the utility of Deng extropy in pattern recognition.

Main Methods:

  • Definition of Deng extropy.
  • Comparative analysis with Deng entropy using examples.
  • Study of Deng extropy's behavior under focal element changes.
  • Characterization of maximum Deng extropy.

Main Results:

  • Deng extropy is formally defined.
  • The relationship between Deng extropy and Deng entropy is explored.
  • The behavior of Deng extropy is characterized.
  • A numerical example illustrates its application in pattern recognition.

Conclusions:

  • Deng extropy is a valid new measure in evidence theory.
  • The study highlights the properties and applications of Deng extropy.
  • Deng extropy shows relevance in pattern recognition tasks.