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Entropy and Semi-Entropies of LR Fuzzy Numbers' Linear Function with Applications to Fuzzy Programming
Jian Zhou1, Chuan Huang1, Mingxuan Zhao2
1School of Management, Shanghai University, Shanghai 200444, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study simplifies entropy calculations for fuzzy programming using credibility theory. New formulas for entropy, semi-entropy, and optimization models are proposed for better decision-making in uncertain environments.
Area of Science:
- Fuzzy mathematics
- Decision science
- Operations research
Background:
- Entropy is key for uncertainty but computationally complex in fuzzy programming.
- Existing methods for entropy in fuzzy numbers are often intricate.
- Need for simplified entropy measures to expand fuzzy programming applications.
Purpose of the Study:
- To investigate entropy within credibility theory for simplified fuzzy number calculations.
- To develop formulas for entropy, semi-entropy, and linear function entropy.
- To propose entropy optimization models for fuzzy programming.
Main Methods:
- Derivation of entropy formulas for regular LR fuzzy numbers using inverse credibility distribution.
- Verification of entropy operator properties.
- Formulation of lower and upper semi-entropies for one-sided uncertainty.
- Development of two entropy optimization models and their equivalent formulations.
Main Results:
- Established formulas for calculating the entropy of regular LR fuzzy numbers.
- Proposed a calculation formula for the entropy of a linear function.
- Introduced lower and upper semi-entropies and their formulas.
- Presented two entropy optimization models for fuzzy programming.
Conclusions:
- The proposed methods offer an effective approach to fuzzy programming using entropy.
- The simplified formulas enhance the applicability of entropy in decision-making.
- Numerical examples confirm the efficiency and performance of the entropy-based models.
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