On the relationship among F-transform, fuzzy rough set and fuzzy topology
Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a spa...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Perfilieva, I. [verfasserIn] Singh, Anand P. [verfasserIn] Tiwari, S. P. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 21(2017), 13 vom: 24. März, Seite 3513-3523 |
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| Übergeordnetes Werk: |
volume:21 ; year:2017 ; number:13 ; day:24 ; month:03 ; pages:3513-3523 |
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| DOI / URN: |
10.1007/s00500-017-2559-x |
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| 520 | |a Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. | ||
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10.1007/s00500-017-2559-x doi (DE-627)SPR006492398 (SPR)s00500-017-2559-x-e DE-627 ger DE-627 rakwb eng Perfilieva, I. verfasserin aut On the relationship among F-transform, fuzzy rough set and fuzzy topology 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. -transform (dpeaa)DE-He213 Fuzzy partition (dpeaa)DE-He213 Residuated lattice (dpeaa)DE-He213 Fuzzy rough set (dpeaa)DE-He213 Fuzzy topology (dpeaa)DE-He213 Fuzzy co-topology (dpeaa)DE-He213 Singh, Anand P. verfasserin aut Tiwari, S. P. verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 21(2017), 13 vom: 24. März, Seite 3513-3523 (DE-627)SPR006469531 nnns volume:21 year:2017 number:13 day:24 month:03 pages:3513-3523 https://dx.doi.org/10.1007/s00500-017-2559-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 21 2017 13 24 03 3513-3523 |
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10.1007/s00500-017-2559-x doi (DE-627)SPR006492398 (SPR)s00500-017-2559-x-e DE-627 ger DE-627 rakwb eng Perfilieva, I. verfasserin aut On the relationship among F-transform, fuzzy rough set and fuzzy topology 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. -transform (dpeaa)DE-He213 Fuzzy partition (dpeaa)DE-He213 Residuated lattice (dpeaa)DE-He213 Fuzzy rough set (dpeaa)DE-He213 Fuzzy topology (dpeaa)DE-He213 Fuzzy co-topology (dpeaa)DE-He213 Singh, Anand P. verfasserin aut Tiwari, S. P. verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 21(2017), 13 vom: 24. März, Seite 3513-3523 (DE-627)SPR006469531 nnns volume:21 year:2017 number:13 day:24 month:03 pages:3513-3523 https://dx.doi.org/10.1007/s00500-017-2559-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 21 2017 13 24 03 3513-3523 |
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10.1007/s00500-017-2559-x doi (DE-627)SPR006492398 (SPR)s00500-017-2559-x-e DE-627 ger DE-627 rakwb eng Perfilieva, I. verfasserin aut On the relationship among F-transform, fuzzy rough set and fuzzy topology 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. -transform (dpeaa)DE-He213 Fuzzy partition (dpeaa)DE-He213 Residuated lattice (dpeaa)DE-He213 Fuzzy rough set (dpeaa)DE-He213 Fuzzy topology (dpeaa)DE-He213 Fuzzy co-topology (dpeaa)DE-He213 Singh, Anand P. verfasserin aut Tiwari, S. P. verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 21(2017), 13 vom: 24. März, Seite 3513-3523 (DE-627)SPR006469531 nnns volume:21 year:2017 number:13 day:24 month:03 pages:3513-3523 https://dx.doi.org/10.1007/s00500-017-2559-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 21 2017 13 24 03 3513-3523 |
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10.1007/s00500-017-2559-x doi (DE-627)SPR006492398 (SPR)s00500-017-2559-x-e DE-627 ger DE-627 rakwb eng Perfilieva, I. verfasserin aut On the relationship among F-transform, fuzzy rough set and fuzzy topology 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. -transform (dpeaa)DE-He213 Fuzzy partition (dpeaa)DE-He213 Residuated lattice (dpeaa)DE-He213 Fuzzy rough set (dpeaa)DE-He213 Fuzzy topology (dpeaa)DE-He213 Fuzzy co-topology (dpeaa)DE-He213 Singh, Anand P. verfasserin aut Tiwari, S. P. verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 21(2017), 13 vom: 24. März, Seite 3513-3523 (DE-627)SPR006469531 nnns volume:21 year:2017 number:13 day:24 month:03 pages:3513-3523 https://dx.doi.org/10.1007/s00500-017-2559-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 21 2017 13 24 03 3513-3523 |
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Perfilieva, I. misc -transform misc Fuzzy partition misc Residuated lattice misc Fuzzy rough set misc Fuzzy topology misc Fuzzy co-topology On the relationship among F-transform, fuzzy rough set and fuzzy topology |
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Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. |
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Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. |
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Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006492398</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002826.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-017-2559-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006492398</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-017-2559-x-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Perfilieva, I.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the relationship among F-transform, fuzzy rough set and fuzzy topology</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct %$F^{\arrow }%$ and %$F^{\downarrow }%$-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-transform</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fuzzy partition</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Residuated lattice</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fuzzy rough set</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fuzzy topology</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fuzzy co-topology</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Singh, Anand P.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tiwari, S. P.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Soft Computing</subfield><subfield code="d">Springer-Verlag, 2003</subfield><subfield code="g">21(2017), 13 vom: 24. März, Seite 3513-3523</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:21</subfield><subfield code="g">year:2017</subfield><subfield code="g">number:13</subfield><subfield code="g">day:24</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:3513-3523</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-017-2559-x</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">21</subfield><subfield code="j">2017</subfield><subfield code="e">13</subfield><subfield code="b">24</subfield><subfield code="c">03</subfield><subfield code="h">3513-3523</subfield></datafield></record></collection>
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