Extension of restricted equivalence functions and similarity measures for type-2 fuzzy sets
| dc.contributor.author | Miguel Turullols, Laura de | |
| dc.contributor.author | Santiago, Regivan | |
| dc.contributor.author | Wagner, Christian | |
| dc.contributor.author | Garibaldi, Jonathan M. | |
| dc.contributor.author | Takáč, Zdenko | |
| dc.contributor.author | Roldán López de Hierro, Antonio Francisco | |
| dc.contributor.author | Bustince Sola, Humberto | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute of Smart Cities - ISC | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.funder | Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa | es |
| dc.date.accessioned | 2022-05-10T11:00:36Z | |
| dc.date.available | 2022-12-17T00:00:17Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | In this work we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence functions allow us to compare any two general type-2 fuzzy sets and to generate a similarity measure for type-2 fuzzy sets. The result of this similarity is a fuzzy set on the same referential set (i.e., domain) as the considered type-2 fuzzy set. The latter is crucial for applications such as explainable AI and decision making, as it enables an intuitive interpretation of the similarity within the domain-specific context of the fuzzy sets. We show how this measure can be used to compare type-2 fuzzy sets with different membership functions in such a way that the uncertainty linked to type-2 fuzzy sets is not lost. This is achieved by generating a fuzzy set rather than a single numerical value. Furthermore, we also show how to obtain a numerical value for discrete referential sets. | en |
| dc.description.sponsorship | This work has been supported by the Research Services of Universidad Pública de Navarra as well as by the Projects PID2019-108392GBI00, financed by MCIN/AEI/10.13039/501100011033), TIN2017-89517-P, by grant VEGA 1/0267/21 and UK EPSRC grant EP/P011918/1. | en |
| dc.embargo.lift | 2022-12-17 | |
| dc.embargo.terms | 2022-12-17 | |
| dc.format.extent | 12 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | L. De Miguel et al., 'Extension of restricted equivalence functions and similarity measures for type-2 fuzzy sets,' in IEEE Transactions on Fuzzy Systems, doi: 10.1109/TFUZZ.2021.3136349. | en |
| dc.identifier.doi | 10.1109/TFUZZ.2021.3136349 | |
| dc.identifier.issn | 1941-0034 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/42915 | |
| dc.language.iso | eng | en |
| dc.publisher | IEEE | en |
| dc.relation.ispartof | IEEE Transactions on Fuzzy Systems (2021) | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108392GB-I00/ES/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TIN2017-89517-P/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1109/TFUZZ.2021.3136349 | |
| dc.rights | © 2021 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 work. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Type-2 fuzzy sets | en |
| dc.subject | Restricted equivalence functions | en |
| dc.subject | Similarity measures | en |
| dc.subject | Uncertainty | en |
| dc.subject | Information loss | en |
| dc.subject | Explainable AI | en |
| dc.title | Extension of restricted equivalence functions and similarity measures for type-2 fuzzy sets | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
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