On Generalized Overlap and Grouping Indices in n-Dimensional Contexts
Abstract Overlap and grouping indices are functions measuring, respectively, the fuzzy intersection and fuzzy union of two fuzzy sets. They have been applied successfully in several fields, such as in interpolative fuzzy systems, fuzzy rule-based classification systems and comparison of fuzzy infere...
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| Format: | Article |
| Language: | English |
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Springer
2025-05-01
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| Series: | International Journal of Computational Intelligence Systems |
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| Online Access: | https://doi.org/10.1007/s44196-025-00796-6 |
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| author | Tiago Asmus Graçaliz Dimuro Giancarlo Lucca Cedric Marco-Detchart Helida Santos Heloisa Camargo Humberto Bustince |
| author_facet | Tiago Asmus Graçaliz Dimuro Giancarlo Lucca Cedric Marco-Detchart Helida Santos Heloisa Camargo Humberto Bustince |
| author_sort | Tiago Asmus |
| collection | DOAJ |
| description | Abstract Overlap and grouping indices are functions measuring, respectively, the fuzzy intersection and fuzzy union of two fuzzy sets. They have been applied successfully in several fields, such as in interpolative fuzzy systems, fuzzy rule-based classification systems and comparison of fuzzy inference rules. Overlap and grouping indices can be built employing overlap and grouping functions, respectively, which are possibly non-associative aggregation functions with features that provide good results when applied to practical bivariate problems. Many studies have generalized the concepts of overlap and grouping functions to be applied in n-dimensional problems. However, the concepts of overlap/grouping indices have not been generalized in similar pattern. Since the associative property may not hold, their application in n-dimensional domains, for comparing more than two fuzzy sets at a time, is not immediate, which limit their application in such contexts. The objective of this paper is to introduce the concepts of n-dimensional and general overlap/grouping indices, with special attention to the development of their construction methods based on generalized overlap/grouping functions. As an application example, we introduce the concept of n-dimensional Jaccard index, with a construction method based on n-dimensional overlap/grouping indices, providing an n-dimensional fuzzy set similarity score. |
| format | Article |
| id | doaj-art-194d546848af43c0a2c54ecae8fa68b9 |
| institution | OA Journals |
| issn | 1875-6883 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj-art-194d546848af43c0a2c54ecae8fa68b92025-08-20T01:49:43ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832025-05-0118111610.1007/s44196-025-00796-6On Generalized Overlap and Grouping Indices in n-Dimensional ContextsTiago Asmus0Graçaliz Dimuro1Giancarlo Lucca2Cedric Marco-Detchart3Helida Santos4Heloisa Camargo5Humberto Bustince6Instituto de Matemática, Estatística e Física, Universidade Federal do Rio GrandeCentro de Ciências Computacionais, Universidade Federal do Rio GrandeCentro de Ciências Sociais e Tecnológicas, Universidade Católica de PelotasDepartamento de Estadística, Informática y Matematicas, Universidad Publica de NavarraCentro de Ciências Computacionais, Universidade Federal do Rio GrandeCentro de Ciências Exatas e de Tecnologia, Universidade Federal de São CarlosDepartamento de Estadística, Informática y Matematicas, Universidad Publica de NavarraAbstract Overlap and grouping indices are functions measuring, respectively, the fuzzy intersection and fuzzy union of two fuzzy sets. They have been applied successfully in several fields, such as in interpolative fuzzy systems, fuzzy rule-based classification systems and comparison of fuzzy inference rules. Overlap and grouping indices can be built employing overlap and grouping functions, respectively, which are possibly non-associative aggregation functions with features that provide good results when applied to practical bivariate problems. Many studies have generalized the concepts of overlap and grouping functions to be applied in n-dimensional problems. However, the concepts of overlap/grouping indices have not been generalized in similar pattern. Since the associative property may not hold, their application in n-dimensional domains, for comparing more than two fuzzy sets at a time, is not immediate, which limit their application in such contexts. The objective of this paper is to introduce the concepts of n-dimensional and general overlap/grouping indices, with special attention to the development of their construction methods based on generalized overlap/grouping functions. As an application example, we introduce the concept of n-dimensional Jaccard index, with a construction method based on n-dimensional overlap/grouping indices, providing an n-dimensional fuzzy set similarity score.https://doi.org/10.1007/s44196-025-00796-6Overlap functionsGrouping functionsOverlap indexGrouping indexJaccard index |
| spellingShingle | Tiago Asmus Graçaliz Dimuro Giancarlo Lucca Cedric Marco-Detchart Helida Santos Heloisa Camargo Humberto Bustince On Generalized Overlap and Grouping Indices in n-Dimensional Contexts International Journal of Computational Intelligence Systems Overlap functions Grouping functions Overlap index Grouping index Jaccard index |
| title | On Generalized Overlap and Grouping Indices in n-Dimensional Contexts |
| title_full | On Generalized Overlap and Grouping Indices in n-Dimensional Contexts |
| title_fullStr | On Generalized Overlap and Grouping Indices in n-Dimensional Contexts |
| title_full_unstemmed | On Generalized Overlap and Grouping Indices in n-Dimensional Contexts |
| title_short | On Generalized Overlap and Grouping Indices in n-Dimensional Contexts |
| title_sort | on generalized overlap and grouping indices in n dimensional contexts |
| topic | Overlap functions Grouping functions Overlap index Grouping index Jaccard index |
| url | https://doi.org/10.1007/s44196-025-00796-6 |
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