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Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces new methods to calculate entropy for fuzzy intervals, improving risk measurement in optimization and expanding applications in LR fuzzy interval theory.
Area of Science:
- Optimization Theory
- Fuzzy Mathematics
- Risk Management
Background:
- Entropy is crucial for risk measurement in optimization, particularly in portfolio management.
- Existing methods for calculating entropy in fuzzy interval theory can be complex.
- There is a need for simplified and efficient entropy calculation methods.
Purpose of the Study:
- To propose simplified calculation formulas for the entropy of functions involving LR fuzzy intervals.
- To develop novel simulation algorithms for calculating the entropy of complex nonlinear functions of LR fuzzy intervals.
- To enhance the applicability of entropy in LR fuzzy interval theory.
Main Methods:
- Developed calculation formulas for entropy using the inverse credibility distribution for linear and simple nonlinear functions.
- Designed two simulation algorithms combining uniform discretization and numerical integration for complex nonlinear functions.
- Validated the proposed methods against existing simulation algorithms.
Main Results:
- The proposed calculation formulas simplify entropy computation for LR fuzzy intervals.
- The novel simulation algorithms demonstrate superior stability, accuracy, and speed compared to existing methods.
- Numerical results confirm the effectiveness of the developed algorithms.
Conclusions:
- The simplified formulas and effective algorithms offer a powerful toolkit for LR fuzzy interval theory.
- This research significantly advances entropy optimization within the LR fuzzy interval framework.
- The findings facilitate more robust risk measurement and decision-making in optimization problems.
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