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Fractional Deng Entropy and Extropy and Some Applications
Mohammad Reza Kazemi1, Saeid Tahmasebi2, Francesco Buono3
1Department of Statistics, Faculty of Science, Fasa University, Fasa 746-168-6688, Iran.
Entropy (Basel, Switzerland)
|June 2, 2021
Summary
This study introduces fractional Deng entropy and extropy, novel measures for quantifying uncertainty within Dempster-Shafer theory (DST). These new fractional measures are analyzed and applied to pattern recognition classification problems.
Area of Science:
- Information Theory
- Artificial Intelligence
- Mathematical Physics
Background:
- Dempster-Shafer theory (DST) utilizes Deng entropy and extropy to quantify uncertainty.
- Extropy is recognized as the dual concept of entropy.
- Existing measures may not fully capture complex uncertainty dynamics.
Purpose of the Study:
- Introduce and define fractional Deng entropy and fractional Deng extropy.
- Compare these new fractional measures with existing uncertainty quantification methods in DST.
- Demonstrate the utility of fractional Deng entropy and extropy in pattern recognition tasks.
Main Methods:
- Development of fractional calculus-based definitions for Deng entropy and extropy.
- Theoretical analysis of the properties of fractional Deng entropy and extropy, including their maxima.
- Application and evaluation of the proposed measures in a pattern recognition classification problem.
Main Results:
- Successfully defined and presented fractional Deng entropy and fractional Deng extropy.
- Demonstrated that fractional Deng entropy and extropy exhibit distinct behaviors and maxima.
- Showcased the effectiveness of the new fractional measures in a classification task, highlighting their importance.
Conclusions:
- Fractional Deng entropy and extropy offer a more nuanced approach to uncertainty quantification in DST.
- These novel measures provide valuable tools for analyzing complex systems, particularly in pattern recognition.
- The study underscores the significance of fractional extensions in information theory and evidence theory.
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