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Divergence and Similarity Characteristics for Two Fuzzy Measures Based on Associated Probabilities

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Názov: Divergence and Similarity Characteristics for Two Fuzzy Measures Based on Associated Probabilities
Autori: Gia Sirbiladze, Bidzina Midodashvili, Teimuraz Manjafarashvili
Zdroj: Axioms, Vol 13, Iss 11, p 776 (2024)
Informácie o vydavateľovi: MDPI AG, 2024.
Rok vydania: 2024
Zbierka: LCC:Mathematics
Predmety: fuzzy measures, associated probabilities, distances, distance generator, divergence indexes, fuzzy measure identification, Mathematics, QA1-939
Popis: The article deals with the definitions of the distance, divergence, and similarity characteristics between two finite fuzzy measures, which are generalizations of the same definitions between two finite probability distributions. As is known, a fuzzy measure can be uniquely represented by the so-called its associated probability class (APC). The idea of generalization is that new definitions of distance, divergence, and similarity between fuzzy measures are reduced to the definitions of distance, divergence, and similarity between the APCs of fuzzy measures. These definitions are based on the concept of distance generator. The proof of the correctness of generalizations is provided. Constructed distance, similarity, and divergence relations can be used in such applied problems as: determining the difference between Dempster-Shafer belief structures; Constructions of collaborative filtering similarity relations; non-additive and interactive parameters of machine learning in phase space metrics definition, object clustering, classification and other tasks. In this work, a new concept is used in the fuzzy measure identification problem for a certain multi-attribute decision-making (MADM) environment. For this, a conditional optimization problem with one objective function representing the distance, divergence or similarity index is formulated. Numerical examples are discussed and a comparative analysis of the obtained results is presented.
Druh dokumentu: article
Popis súboru: electronic resource
Jazyk: English
ISSN: 2075-1680
Relation: https://www.mdpi.com/2075-1680/13/11/776; https://doaj.org/toc/2075-1680
DOI: 10.3390/axioms13110776
Prístupová URL adresa: https://doaj.org/article/024c491e47e346e08cd8bfbfbfd7620b
Prístupové číslo: edsdoj.024c491e47e346e08cd8bfbfbfd7620b
Databáza: Directory of Open Access Journals
Popis
Abstrakt:The article deals with the definitions of the distance, divergence, and similarity characteristics between two finite fuzzy measures, which are generalizations of the same definitions between two finite probability distributions. As is known, a fuzzy measure can be uniquely represented by the so-called its associated probability class (APC). The idea of generalization is that new definitions of distance, divergence, and similarity between fuzzy measures are reduced to the definitions of distance, divergence, and similarity between the APCs of fuzzy measures. These definitions are based on the concept of distance generator. The proof of the correctness of generalizations is provided. Constructed distance, similarity, and divergence relations can be used in such applied problems as: determining the difference between Dempster-Shafer belief structures; Constructions of collaborative filtering similarity relations; non-additive and interactive parameters of machine learning in phase space metrics definition, object clustering, classification and other tasks. In this work, a new concept is used in the fuzzy measure identification problem for a certain multi-attribute decision-making (MADM) environment. For this, a conditional optimization problem with one objective function representing the distance, divergence or similarity index is formulated. Numerical examples are discussed and a comparative analysis of the obtained results is presented.
ISSN:20751680
DOI:10.3390/axioms13110776