Year: 2025
Type: article
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.
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,490
Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul, Universidad Pública de Navarra, Agencia Estatal de Investigación
Awards: G1312179244, Achieving the Sustainable Development Goals in the context of dealing with disasters (CODeS): computational tools in integrated data analysis, G1739013769, G1830353648, G1832552119, G3480869486, G4401948155, G4526231891, G4803042526, G4911562169, G5080475149, G572068088, G6239515261, G6794256107, G6990889504, G7084143925
OpenAlex ID: W4410214067