The approximation of left-continuous t-norms

A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Fuzzy sets and systems 2016-06, Vol.292, p.411-423
1. Verfasser:	Vetterlein, Thomas
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Approximation Fuzzy set theory Intervals Mathematical analysis
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	423
container_issue
container_start_page	411
container_title	Fuzzy sets and systems
container_volume	292
creator	Vetterlein, Thomas
description	A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision.
doi_str_mv	10.1016/j.fss.2014.07.002
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1816011936</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0165011414003091</els_id><sourcerecordid>1816011936</sourcerecordid><originalsourceid>FETCH-LOGICAL-c282t-c81ab9b139839b22a74dff6487c8529b98ddcabb69045c973304968da023b4c33</originalsourceid><addsrcrecordid>eNp9kD1PwzAQhi0EEqXwA9gyMpBwZ7uJLSZU8SVVYimzZTu2cJXGxU4R_HtclZnpbnif03sPIdcIDQK2d5vG59xQQN5A1wDQEzJD0dG6FYCnZFYyixoQ-Tm5yHkDUPYWZuR2_eEqvdul-B22egpxrKKvBuen2sZxCuM-7nM11WNM23xJzrwesrv6m3Py_vS4Xr7Uq7fn1-XDqrZU0AIK1EYaZFIwaSjVHe-9b7norFhQaaToe6uNaSXwhZUdY8BlK3oNlBluGZuTm-PdUutz7_KktiFbNwx6dKWOQlG6I0rWligeozbFnJPzapfKI-lHIaiDGbVRxYw6mFHQqWKmMPdHxpUfvoJLKtvgRuv6kJydVB_DP_QvDaRqdw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1816011936</pqid></control><display><type>article</type><title>The approximation of left-continuous t-norms</title><source>ScienceDirect Journals (5 years ago - present)</source><creator>Vetterlein, Thomas</creator><creatorcontrib>Vetterlein, Thomas</creatorcontrib><description>A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision.</description><identifier>ISSN: 0165-0114</identifier><identifier>EISSN: 1872-6801</identifier><identifier>DOI: 10.1016/j.fss.2014.07.002</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Algebra ; Approximation ; Fuzzy set theory ; Intervals ; Mathematical analysis</subject><ispartof>Fuzzy sets and systems, 2016-06, Vol.292, p.411-423</ispartof><rights>2014 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c282t-c81ab9b139839b22a74dff6487c8529b98ddcabb69045c973304968da023b4c33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0165011414003091$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Vetterlein, Thomas</creatorcontrib><title>The approximation of left-continuous t-norms</title><title>Fuzzy sets and systems</title><description>A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision.</description><subject>Algebra</subject><subject>Approximation</subject><subject>Fuzzy set theory</subject><subject>Intervals</subject><subject>Mathematical analysis</subject><issn>0165-0114</issn><issn>1872-6801</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwA9gyMpBwZ7uJLSZU8SVVYimzZTu2cJXGxU4R_HtclZnpbnif03sPIdcIDQK2d5vG59xQQN5A1wDQEzJD0dG6FYCnZFYyixoQ-Tm5yHkDUPYWZuR2_eEqvdul-B22egpxrKKvBuen2sZxCuM-7nM11WNM23xJzrwesrv6m3Py_vS4Xr7Uq7fn1-XDqrZU0AIK1EYaZFIwaSjVHe-9b7norFhQaaToe6uNaSXwhZUdY8BlK3oNlBluGZuTm-PdUutz7_KktiFbNwx6dKWOQlG6I0rWligeozbFnJPzapfKI-lHIaiDGbVRxYw6mFHQqWKmMPdHxpUfvoJLKtvgRuv6kJydVB_DP_QvDaRqdw</recordid><startdate>20160601</startdate><enddate>20160601</enddate><creator>Vetterlein, Thomas</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20160601</creationdate><title>The approximation of left-continuous t-norms</title><author>Vetterlein, Thomas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c282t-c81ab9b139839b22a74dff6487c8529b98ddcabb69045c973304968da023b4c33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algebra</topic><topic>Approximation</topic><topic>Fuzzy set theory</topic><topic>Intervals</topic><topic>Mathematical analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vetterlein, Thomas</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Fuzzy sets and systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vetterlein, Thomas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The approximation of left-continuous t-norms</atitle><jtitle>Fuzzy sets and systems</jtitle><date>2016-06-01</date><risdate>2016</risdate><volume>292</volume><spage>411</spage><epage>423</epage><pages>411-423</pages><issn>0165-0114</issn><eissn>1872-6801</eissn><abstract>A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.fss.2014.07.002</doi><tpages>13</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 0165-0114
ispartof	Fuzzy sets and systems, 2016-06, Vol.292, p.411-423
issn	0165-0114 1872-6801
language	eng
recordid	cdi_proquest_miscellaneous_1816011936
source	ScienceDirect Journals (5 years ago - present)
subjects	Algebra Approximation Fuzzy set theory Intervals Mathematical analysis
title	The approximation of left-continuous t-norms
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-01T19%3A53%3A01IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20approximation%20of%20left-continuous%20t-norms&rft.jtitle=Fuzzy%20sets%20and%20systems&rft.au=Vetterlein,%20Thomas&rft.date=2016-06-01&rft.volume=292&rft.spage=411&rft.epage=423&rft.pages=411-423&rft.issn=0165-0114&rft.eissn=1872-6801&rft_id=info:doi/10.1016/j.fss.2014.07.002&rft_dat=%3Cproquest_cross%3E1816011936%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1816011936&rft_id=info:pmid/&rft_els_id=S0165011414003091&rfr_iscdi=true