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A Variation of the Algorithm to Achieve the Maximum Entropy for Belief Functions
Joaquín Abellán1, Alejandro Pérez-Lara1, Serafín Moral-García1
1Department of Computer Science and Artificial Intelligence, University of Granada, 18014 Granada, Spain.
Entropy (Basel, Switzerland)
|June 28, 2023
Summary
Evidence theory (TE) uses maximum of entropy (ME) to quantify information, but its computation is complex. This study presents a modified algorithm that reduces computational steps, enhancing the applicability of ME in TE for incomplete information scenarios.
Area of Science:
- Information Theory
- Decision Science
- Mathematical Foundations
Background:
- Classical probability theory (PT) struggles with inaccurate or incomplete information.
- Evidence theory (TE) offers a framework for imprecise probabilities, with maximum of entropy (ME) quantifying evidence.
- The computational complexity of ME has limited its practical application in TE.
Purpose of the Study:
- To address the computational challenges associated with calculating the maximum of entropy (ME) in Evidence Theory (TE).
- To propose a modified algorithm for ME calculation that improves efficiency.
- To enhance the practical applicability of ME in TE for real-world problems involving uncertain data.
Main Methods:
- A variation of the existing algorithm for calculating the maximum of entropy (ME) in Evidence Theory (TE) was developed.
- The modified algorithm focuses on reducing the size of the power set of possibilities at each computational step.
- The efficiency of the new algorithm was analyzed in terms of the number of computational steps required.
Main Results:
- The modified algorithm significantly reduces the number of steps needed to compute the maximum of entropy (ME).
- By reducing the power set size iteratively, the computational cost is lowered.
- The proposed variation offers a more efficient approach to ME calculation within TE.
Conclusions:
- The modified algorithm provides a more computationally tractable method for determining the maximum of entropy (ME) in Evidence Theory (TE).
- This improvement is expected to increase the adoption and utility of ME for information quantification in TE.
- The research facilitates broader application of TE in domains characterized by imprecise or incomplete data.
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