Fuzzifying bornological linear spaces
In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are s...
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| Published in | Journal of intelligent & fuzzy systems Vol. 42; no. 3; pp. 2347 - 2358 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
London, England
SAGE Publications
01.01.2022
Sage Publications Ltd |
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| Abstract | In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided. |
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| AbstractList | In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided. |
| Author | Yan, Cong-Hua Jin, Zhen-Yu |
| Author_xml | – sequence: 1 givenname: Zhen-Yu surname: Jin fullname: Jin, Zhen-Yu organization: Institute of Math., School of Math. Sciences – sequence: 2 givenname: Cong-Hua surname: Yan fullname: Yan, Cong-Hua email: chyan@njnu.edu.cn organization: Institute of Math., School of Math. Sciences |
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| CitedBy_id | crossref_primary_10_1007_s40314_025_03086_1 crossref_primary_10_3934_math_2022916 crossref_primary_10_1016_j_fss_2023_02_017 crossref_primary_10_1515_math_2024_0110 crossref_primary_10_15672_hujms_1264856 crossref_primary_10_1016_j_fss_2024_109175 crossref_primary_10_1016_j_fss_2022_11_007 |
| Cites_doi | 10.1007/978-94-015-9540-7 10.1007/978-94-017-1560-7 10.1016/j.fss.2015.07.016 10.2298/FIL1307345O 10.1016/0165-0114(91)90100-5 10.1007/s11228-008-0086-8 10.1016/j.jmaa.2008.03.058 10.1016/j.jmaa.2014.04.033 10.1016/j.fss.2007.03.017 10.1016/j.jmaa.2004.04.046 10.1007/978-1-4684-9928-5_1 10.1016/j.jmaa.2007.07.010 10.1016/j.jmaa.2010.05.042 10.1016/j.fss.2003.10.024 10.2140/pjm.1960.10.313 10.1016/j.topol.2008.12.030 10.1016/j.fss.2014.09.006 10.1016/j.fss.2013.07.013 10.1016/j.topol.2011.04.025 10.2140/pjm.1968.24.437 10.1007/978-3-319-66827-7_41 10.1016/0165-0114(91)90164-L |
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| Copyright | 2022 – IOS Press. All rights reserved Copyright IOS Press BV 2022 |
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| Issue | 3 |
| Keywords | quotient linear fuzzifying bornologies separation fuzzifying bornological convergence Fuzzifying bornological linear spaces Product linear fuzzifying bornologies |
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| References | 2007; 158 2004; 297 1968; 24 2014; 238 2014; 419 1960; 10 1991; 39 2004; 147 2013; 27 2015; 259 2008; 16 2001; 8 1949; 28 1991; 40 2008; 339 2009; 156 158 2010; 371 2009; 350 1970; 94 2012; 159 2011; 8 2016; 294 Beer (10.3233/JIFS-211644_ref5) 2009; 156 Egbert (10.3233/JIFS-211644_ref12) 1968; 24 10.3233/JIFS-211644_ref13 Beer (10.3233/JIFS-211644_ref4) 2008; 16 10.3233/JIFS-211644_ref17 Šostak (10.3233/JIFS-211644_ref26) 2016; 294 Beer (10.3233/JIFS-211644_ref2) 2001; 8 Qiu (10.3233/JIFS-211644_ref22) 2004; 147 Beer (10.3233/JIFS-211644_ref3) 2008; 339 Abel (10.3233/JIFS-211644_ref1) 2011; 8 Caserta (10.3233/JIFS-211644_ref10) 2012; 159 Osçag (10.3233/JIFS-211644_ref19) 2013; 27 Caserta (10.3233/JIFS-211644_ref9) 2010; 371 Yan (10.3233/JIFS-211644_ref28) 2007; 158 Yan (10.3233/JIFS-211644_ref29) 2014; 238 Paseka (10.3233/JIFS-211644_ref21) 2015; 259 Lechicki (10.3233/JIFS-211644_ref18) 2004; 297 10.3233/JIFS-211644_ref25 Hu (10.3233/JIFS-211644_ref15) 1949; 28 10.3233/JIFS-211644_ref27 Rodabaugh (10.3233/JIFS-211644_ref23) 1991; 40 Yan (10.3233/JIFS-211644_ref30); 158 Ying (10.3233/JIFS-211644_ref31) 1991; 39 Blyth (10.3233/JIFS-211644_ref8) 1970; 94 Beer (10.3233/JIFS-211644_ref6) 2009; 350 Schweizer (10.3233/JIFS-211644_ref24) 1960; 10 Paseka (10.3233/JIFS-211644_ref20) 2014; 419 |
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volume: 294 start-page: 93 year: 2016 ident: 10.3233/JIFS-211644_ref26 article-title: L-valued bornologies onpowersets publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2015.07.016 – volume: 27 start-page: 1345 issue: 7 year: 2013 ident: 10.3233/JIFS-211644_ref19 article-title: Bornologies and bitopological function spaces publication-title: Filomat doi: 10.2298/FIL1307345O – volume: 8 start-page: 273 year: 2001 ident: 10.3233/JIFS-211644_ref2 article-title: Metric bornologies and Kuratowska-Painlevé convergenceto the empty set publication-title: Journal of Convex Analysis – volume: 94 start-page: 101 year: 1970 ident: 10.3233/JIFS-211644_ref8 article-title: Sur certaines images homomorphes des demi-groupes ordonns publication-title: Bulletin de la Soci&t& Math&matique de France – volume: 39 start-page: 303 year: 1991 ident: 10.3233/JIFS-211644_ref31 article-title: A new approach for fuzzy topology (I) publication-title: Fuzzy Sets andSystems doi: 10.1016/0165-0114(91)90100-5 – volume: 16 start-page: 489 year: 2008 ident: 10.3233/JIFS-211644_ref4 article-title: Gap, excess and bornological convergence publication-title: Set-Valued Analysis doi: 10.1007/s11228-008-0086-8 – volume: 350 start-page: 568 year: 2009 ident: 10.3233/JIFS-211644_ref6 article-title: Strong uniform continuity publication-title: Journal ofMathematical Analysis and Applications doi: 10.1016/j.jmaa.2008.03.058 – volume: 419 start-page: 138 year: 2014 ident: 10.3233/JIFS-211644_ref20 article-title: On the category oflattice-valued bornological vector spaces publication-title: Journal ofMathematical Analysis and Applications doi: 10.1016/j.jmaa.2014.04.033 – volume: 158 start-page: 1803 year: 2007 ident: 10.3233/JIFS-211644_ref28 article-title: Level topologies of fuzzifying topological linear spaces andtheir applications publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2007.03.017 – volume: 297 start-page: 751 year: 2004 ident: 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Boundedness in a topological space publication-title: Journal de Mathĺęmatiques Pures et Appliquées – volume: 147 start-page: 249 year: 2004 ident: 10.3233/JIFS-211644_ref22 article-title: Fuzzifying topological linear spaces publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2003.10.024 – volume: 10 start-page: 313 year: 1960 ident: 10.3233/JIFS-211644_ref24 article-title: Statistical metric spaces publication-title: Pacific Journal of Mathematics doi: 10.2140/pjm.1960.10.313 – volume: 156 start-page: 1271 year: 2009 ident: 10.3233/JIFS-211644_ref5 article-title: Total boundedness and bornology publication-title: Topologyand Applications doi: 10.1016/j.topol.2008.12.030 – volume: 259 start-page: 68 year: 2015 ident: 10.3233/JIFS-211644_ref21 article-title: Lattice-valuedbornological systems publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2014.09.006 – volume: 238 start-page: 89 year: 2014 ident: 10.3233/JIFS-211644_ref29 article-title: Fuzzifying topologies on the space of linear operators publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2013.07.013 – volume: 159 start-page: 1847 year: 2012 ident: 10.3233/JIFS-211644_ref10 article-title: Bornologies, selectionprinciples and function spaces publication-title: Topology and Applications doi: 10.1016/j.topol.2011.04.025 – volume: 24 start-page: 437 year: 1968 ident: 10.3233/JIFS-211644_ref12 article-title: Products and quotients of probabilistic metric spaces publication-title: Pacific Journal of Mathematics doi: 10.2140/pjm.1968.24.437 – ident: 10.3233/JIFS-211644_ref27 doi: 10.1007/978-3-319-66827-7_41 – volume: 158 start-page: 937 issue: 2007 ident: 10.3233/JIFS-211644_ref30 article-title: Continuity of linear operators in L-fuzzifyingtopological vector spaces publication-title: Fuzzy Sets and Systems – volume: 40 start-page: 297 year: 1991 ident: 10.3233/JIFS-211644_ref23 article-title: Point-set lattice-theoretic topology publication-title: FuzzySets and Systems doi: 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