Conference paper Open Access

# On the standard fuzzy metric: generalizations and application to model estimation

Juan José Miñana; Alberto Ortiz; Esaú Ortiz; Óscar Valero

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<identifier identifierType="DOI">10.5281/zenodo.4964783</identifier>
<creators>
<creator>
<creatorName>Juan José Miñana</creatorName>
<affiliation>University of the Balearic Islands</affiliation>
</creator>
<creator>
<creatorName>Alberto Ortiz</creatorName>
<affiliation>University of the Balearic Islands</affiliation>
</creator>
<creator>
<creatorName>Esaú Ortiz</creatorName>
<affiliation>University of the Balearic Islands</affiliation>
</creator>
<creator>
<creatorName>Óscar Valero</creatorName>
<affiliation>University of the Balearic Islands</affiliation>
</creator>
</creators>
<titles>
<title>On the standard fuzzy metric: generalizations and application to model estimation</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2021</publicationYear>
<subjects>
<subject>fuzzy metrics</subject>
<subject>RANSAC</subject>
<subject>model estimation</subject>
</subjects>
<dates>
<date dateType="Issued">2021-06-16</date>
</dates>
<resourceType resourceTypeGeneral="ConferencePaper"/>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/4964783</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.4964782</relatedIdentifier>
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<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract">&lt;p&gt;Different approaches to obtain a notion of metric in the context of fuzzy setting can be found in the literature. In this paper, we deal with the concept due to George and Veeramani, which is defined by means of continuous triangular norms. Different authors have addressed the study of such a concept from a theoretical point of view. In this paper, we provide a new methodology to induce fuzzy metrics which generalize the celebrated standard fuzzy metric. The aforementioned methodology allows us to approach some questions related to the continuous triangular norms from which such fuzzy metrics are defined. Morever, we show the applicability of the new fuzzy metrics to an engineering problem. More specifically, we address successfully robust model estimation through a variant of the well-known estimator RANSAC. By way of illustration of the performance of the approach, we report on the accuracy achieved by the new estimator and other RANSAC variants for a benchmark involving a specific model estimation problem and a large number of datasets with varying proportion of outliers and different levels of noise. The resulting estimator is shown able to outperform the classical counterparts considered.&lt;/p&gt;</description>
<description descriptionType="Other">This work is also supported by project PGC2018-095709-B-C21 (MCIU/AEI/FEDER, UE), and PROCOE/4/2017 (Govern Balear, 50% P.O. FEDER 2014-2020 Illes Balears).</description>
</descriptions>
<fundingReferences>
<fundingReference>
<funderName>European Commission</funderName>
<funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
<awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/779776/">779776</awardNumber>
<awardTitle>Robotics Technology for Inspection of Ships</awardTitle>
</fundingReference>
<fundingReference>
<funderName>European Commission</funderName>
<funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
<awardNumber awardURI="info:eu-repo/grantAgreement/EC/Horizon 2020 Framework Programme - Innovation action/871260/">871260</awardNumber>
<awardTitle>Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanks</awardTitle>
</fundingReference>
</fundingReferences>
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