Ferrero Jaurrieta, MikelTakáč, ZdenkoRodríguez Martínez, IosuMarco Detchart, CedricBernardini, ÁngelaFernández Fernández, Francisco JavierLópez Molina, CarlosBustince Sola, Humberto2023-05-052023-05-052023Ferrero-Jaurrieta, M., Takac, Z., Rodríguez-Martínez, I., Marco-Detchart, C., Bernardini, A., Fernández-Fernández, J., Lopez-Molina, C., Bustince, H. (2023) From restricted equivalence functions on Ln to similarity measures between fuzzy multisets. IEEE Transactions on Fuzzy Systems, 1-14. https://doi.org/10.1109/TFUZZ.2023.3235405.1063-670610.1109/TFUZZ.2023.3235405https://academica-e.unavarra.es/handle/2454/45222Versión resumida en castellano: https://academica-e.unavarra.es/handle/2454/53327Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from L to L n and present a new similarity construction on L n . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.application/pdfeng© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other workAnisotropic diffusionColorColor imageFuzzy multisetFuzzy set theoryFuzzy setsImage color analysisProposalsRestricted equivalence functionSimilarity measureTask analysisTaxonomyinfo:eu-repo/semantics/article2023-05-05info:eu-repo/semantics/openAccess