Fixed points of involutive interval-valued negations
Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely deter...
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| Veröffentlicht in: | Fuzzy sets and systems 2011-11, Vol.182 (1), p.110-118 |
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| creator | Wu, Jiachao Luo, Maokang |
| description | Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained.
► All the fixed points of an involutive interval-valued negation are characterized. ► The definitions of the imaginary fixed points and of the fixed point function are given. ► An involutive interval-valued negation is characterized by its fixed points. ► As an application of the fixed point function, a representative theorem of an involutive interval-valued negation is constructed. |
| doi_str_mv | 10.1016/j.fss.2011.05.029 |
| format | Article |
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► All the fixed points of an involutive interval-valued negation are characterized. ► The definitions of the imaginary fixed points and of the fixed point function are given. ► An involutive interval-valued negation is characterized by its fixed points. ► As an application of the fixed point function, a representative theorem of an involutive interval-valued negation is constructed.</description><identifier>ISSN: 0165-0114</identifier><identifier>EISSN: 1872-6801</identifier><identifier>DOI: 10.1016/j.fss.2011.05.029</identifier><identifier>CODEN: FSSYD8</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Applied sciences ; Circuit properties ; Computer science; control theory; systems ; Construction ; Digital circuits ; Electric, optical and optoelectronic circuits ; Electronic circuits ; Electronics ; Exact sciences and technology ; Fixed points ; Fuzzy set theory ; Global analysis, analysis on manifolds ; Information, signal and communications theory ; Interval-valued negations ; Involutive interval-valued negations ; Mathematical methods ; Mathematics ; Miscellaneous ; Representations ; Sciences and techniques of general use ; Telecommunications and information theory ; Theoretical computing ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Fuzzy sets and systems, 2011-11, Vol.182 (1), p.110-118</ispartof><rights>2011 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-79ad26f85d362e71815c08efc68d86bae77a44dc3cb0834a7b1e0558da68cbbc3</citedby><cites>FETCH-LOGICAL-c359t-79ad26f85d362e71815c08efc68d86bae77a44dc3cb0834a7b1e0558da68cbbc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0165011411002739$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24512959$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Wu, Jiachao</creatorcontrib><creatorcontrib>Luo, Maokang</creatorcontrib><title>Fixed points of involutive interval-valued negations</title><title>Fuzzy sets and systems</title><description>Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained.
► All the fixed points of an involutive interval-valued negation are characterized. ► The definitions of the imaginary fixed points and of the fixed point function are given. ► An involutive interval-valued negation is characterized by its fixed points. ► As an application of the fixed point function, a representative theorem of an involutive interval-valued negation is constructed.</description><subject>Applied sciences</subject><subject>Circuit properties</subject><subject>Computer science; control theory; systems</subject><subject>Construction</subject><subject>Digital circuits</subject><subject>Electric, optical and optoelectronic circuits</subject><subject>Electronic circuits</subject><subject>Electronics</subject><subject>Exact sciences and technology</subject><subject>Fixed points</subject><subject>Fuzzy set theory</subject><subject>Global analysis, analysis on manifolds</subject><subject>Information, signal and communications theory</subject><subject>Interval-valued negations</subject><subject>Involutive interval-valued negations</subject><subject>Mathematical methods</subject><subject>Mathematics</subject><subject>Miscellaneous</subject><subject>Representations</subject><subject>Sciences and techniques of general use</subject><subject>Telecommunications and information theory</subject><subject>Theoretical computing</subject><subject>Topology. 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Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Jiachao</creatorcontrib><creatorcontrib>Luo, Maokang</creatorcontrib><collection>Pascal-Francis</collection><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>Wu, Jiachao</au><au>Luo, Maokang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fixed points of involutive interval-valued negations</atitle><jtitle>Fuzzy sets and systems</jtitle><date>2011-11-01</date><risdate>2011</risdate><volume>182</volume><issue>1</issue><spage>110</spage><epage>118</epage><pages>110-118</pages><issn>0165-0114</issn><eissn>1872-6801</eissn><coden>FSSYD8</coden><abstract>Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained.
► All the fixed points of an involutive interval-valued negation are characterized. ► The definitions of the imaginary fixed points and of the fixed point function are given. ► An involutive interval-valued negation is characterized by its fixed points. ► As an application of the fixed point function, a representative theorem of an involutive interval-valued negation is constructed.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.fss.2011.05.029</doi><tpages>9</tpages></addata></record> |
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| subjects | Applied sciences Circuit properties Computer science control theory systems Construction Digital circuits Electric, optical and optoelectronic circuits Electronic circuits Electronics Exact sciences and technology Fixed points Fuzzy set theory Global analysis, analysis on manifolds Information, signal and communications theory Interval-valued negations Involutive interval-valued negations Mathematical methods Mathematics Miscellaneous Representations Sciences and techniques of general use Telecommunications and information theory Theoretical computing Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Fixed points of involutive interval-valued negations |
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