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Some Theoretical Foundations of Bare-Simulation Optimization of Some Directed Distances between Fuzzy Sets
Michel Broniatowski1, Wolfgang Stummer2
1Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, 4 Place Jussieu, 75252 Paris, France.
This study introduces generalized φ-divergences for measuring dissimilarity between various fuzzy set types and basic belief assignments. A novel bare simulation method efficiently solves associated constrained optimization problems.
Area of Science:
- Information theory
- Statistics
- Machine learning
- Artificial intelligence
Background:
- Quantifying information dissimilarity is crucial in information theory and related fields.
- Constrained optimization is essential for handling imprecise or vague data.
Purpose of the Study:
- Define generalized φ-divergences for fuzzy sets, ν-rung orthopair fuzzy sets, and basic belief assignments.
- Develop methods to solve constrained minimization problems involving these divergences.
Main Methods:
- Definition of generalized φ-divergences for fuzzy set types and basic belief assignments.
- Application of the dimension-free bare (pure) simulation method for optimization.
- Rescaling of basic belief assignments for divergence calculations.
Main Results:
- Successful definition of generalized φ-divergences across multiple fuzzy set representations.
- Demonstration of the bare simulation method's efficacy in solving constrained minimization problems.
- Extension of the approach to basic belief assignments.
Conclusions:
- Generalized φ-divergences provide a robust measure for information dissimilarity.
- The bare simulation method offers an efficient approach to optimization problems in information theory.
- The framework is applicable to diverse data representations, including fuzzy sets and belief assignments.
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