Some Theoretical Foundations of Bare-Simulation Optimization of Some Directed Distances between Fuzzy Sets Respectively Basic Belief Assignments
Broniatowski M, Stummer W (2024)
Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 26
Article Number: 312
Journal Issue: 4
DOI: 10.3390/e26040312
Abstract
It is well known that in information theory—as well as in the adjacent fields of statistics, machine learning and artificial intelligence—it is essential to quantify the dissimilarity between objects of uncertain/imprecise/inexact/vague information; correspondingly, constrained optimization is of great importance, too. In view of this, we define the dissimilarity-measure-natured generalized φ–divergences between fuzzy sets, (Formula presented.) –rung orthopair fuzzy sets, extended representation type (Formula presented.) –rung orthopair fuzzy sets as well as between those fuzzy set types and vectors. For those, we present how to tackle corresponding constrained minimization problems by appropriately applying our recently developed dimension-free bare (pure) simulation method. An analogous program is carried out by defining and optimizing generalized φ–divergences between (rescaled) basic belief assignments as well as between (rescaled) basic belief assignments and vectors.
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APA:
Broniatowski, M., & Stummer, W. (2024). Some Theoretical Foundations of Bare-Simulation Optimization of Some Directed Distances between Fuzzy Sets Respectively Basic Belief Assignments. Entropy, 26(4). https://doi.org/10.3390/e26040312
MLA:
Broniatowski, Michel, and Wolfgang Stummer. "Some Theoretical Foundations of Bare-Simulation Optimization of Some Directed Distances between Fuzzy Sets Respectively Basic Belief Assignments." Entropy 26.4 (2024).
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