Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation
Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gul, Rizwan [verfasserIn] Shabir, Muhammad [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Computational and applied mathematics - Berlin : Springer, 2003, 39(2020), 3 vom: 01. Juni |
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| Übergeordnetes Werk: |
volume:39 ; year:2020 ; number:3 ; day:01 ; month:06 |
| Links: |
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| DOI / URN: |
10.1007/s40314-020-01174-y |
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| Katalog-ID: |
SPR039902951 |
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| 245 | 1 | 0 | |a Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation |
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| 520 | |a Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. | ||
| 650 | 4 | |a Fuzzy set |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Rough set |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bipolar fuzzy set |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bipolar fuzzy tolerance relation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a ( |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a )-Indiscernibility |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a ( |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a )-Bipolar fuzzified rough approximations |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Shabir, Muhammad |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Computational and applied mathematics |d Berlin : Springer, 2003 |g 39(2020), 3 vom: 01. Juni |w (DE-627)47617502X |w (DE-600)2171678-X |x 1807-0302 |7 nnns |
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10.1007/s40314-020-01174-y doi (DE-627)SPR039902951 (SPR)s40314-020-01174-y-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Gul, Rizwan verfasserin aut Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. Fuzzy set (dpeaa)DE-He213 Rough set (dpeaa)DE-He213 Bipolar fuzzy set (dpeaa)DE-He213 Bipolar fuzzy tolerance relation (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Indiscernibility (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Bipolar fuzzified rough approximations (dpeaa)DE-He213 Shabir, Muhammad verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 3 vom: 01. Juni (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:3 day:01 month:06 https://dx.doi.org/10.1007/s40314-020-01174-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE 31.80 ASE AR 39 2020 3 01 06 |
| spelling |
10.1007/s40314-020-01174-y doi (DE-627)SPR039902951 (SPR)s40314-020-01174-y-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Gul, Rizwan verfasserin aut Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. Fuzzy set (dpeaa)DE-He213 Rough set (dpeaa)DE-He213 Bipolar fuzzy set (dpeaa)DE-He213 Bipolar fuzzy tolerance relation (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Indiscernibility (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Bipolar fuzzified rough approximations (dpeaa)DE-He213 Shabir, Muhammad verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 3 vom: 01. Juni (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:3 day:01 month:06 https://dx.doi.org/10.1007/s40314-020-01174-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE 31.80 ASE AR 39 2020 3 01 06 |
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10.1007/s40314-020-01174-y doi (DE-627)SPR039902951 (SPR)s40314-020-01174-y-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Gul, Rizwan verfasserin aut Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. Fuzzy set (dpeaa)DE-He213 Rough set (dpeaa)DE-He213 Bipolar fuzzy set (dpeaa)DE-He213 Bipolar fuzzy tolerance relation (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Indiscernibility (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Bipolar fuzzified rough approximations (dpeaa)DE-He213 Shabir, Muhammad verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 3 vom: 01. Juni (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:3 day:01 month:06 https://dx.doi.org/10.1007/s40314-020-01174-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE 31.80 ASE AR 39 2020 3 01 06 |
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10.1007/s40314-020-01174-y doi (DE-627)SPR039902951 (SPR)s40314-020-01174-y-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Gul, Rizwan verfasserin aut Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. Fuzzy set (dpeaa)DE-He213 Rough set (dpeaa)DE-He213 Bipolar fuzzy set (dpeaa)DE-He213 Bipolar fuzzy tolerance relation (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Indiscernibility (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Bipolar fuzzified rough approximations (dpeaa)DE-He213 Shabir, Muhammad verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 3 vom: 01. Juni (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:3 day:01 month:06 https://dx.doi.org/10.1007/s40314-020-01174-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE 31.80 ASE AR 39 2020 3 01 06 |
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10.1007/s40314-020-01174-y doi (DE-627)SPR039902951 (SPR)s40314-020-01174-y-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Gul, Rizwan verfasserin aut Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. Fuzzy set (dpeaa)DE-He213 Rough set (dpeaa)DE-He213 Bipolar fuzzy set (dpeaa)DE-He213 Bipolar fuzzy tolerance relation (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Indiscernibility (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Bipolar fuzzified rough approximations (dpeaa)DE-He213 Shabir, Muhammad verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 3 vom: 01. Juni (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:3 day:01 month:06 https://dx.doi.org/10.1007/s40314-020-01174-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE 31.80 ASE AR 39 2020 3 01 06 |
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Enthalten in Computational and applied mathematics 39(2020), 3 vom: 01. Juni volume:39 year:2020 number:3 day:01 month:06 |
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Gul, Rizwan @@aut@@ Shabir, Muhammad @@aut@@ |
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Gul, Rizwan |
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510 ASE 31.76 bkl 31.80 bkl Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation Fuzzy set (dpeaa)DE-He213 Rough set (dpeaa)DE-He213 Bipolar fuzzy set (dpeaa)DE-He213 Bipolar fuzzy tolerance relation (dpeaa)DE-He213 ( (dpeaa)DE-He213 )-Indiscernibility (dpeaa)DE-He213 )-Bipolar fuzzified rough approximations (dpeaa)DE-He213 |
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ddc 510 bkl 31.76 bkl 31.80 misc Fuzzy set misc Rough set misc Bipolar fuzzy set misc Bipolar fuzzy tolerance relation misc ( misc )-Indiscernibility misc )-Bipolar fuzzified rough approximations |
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ddc 510 bkl 31.76 bkl 31.80 misc Fuzzy set misc Rough set misc Bipolar fuzzy set misc Bipolar fuzzy tolerance relation misc ( misc )-Indiscernibility misc )-Bipolar fuzzified rough approximations |
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Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation |
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Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation |
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Gul, Rizwan |
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Gul, Rizwan Shabir, Muhammad |
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roughness of a set by %$(\alpha , \beta )%$-indiscernibility of bipolar fuzzy relation |
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Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation |
| abstract |
Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. |
| abstractGer |
Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. |
| abstract_unstemmed |
Abstract In this article, we introduce a new technique for roughness of a set based on %$(\alpha , \beta )%$-indiscernibility, that is, objects are indiscernible up to certain degrees %$\alpha %$ and %$\beta %$. For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for %$(\alpha , \beta )%$-bipolar fuzzified rough set. |
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| title_short |
Roughness of a set by %$(\alpha , \beta )%$-indiscernibility of Bipolar fuzzy relation |
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https://dx.doi.org/10.1007/s40314-020-01174-y |
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Shabir, Muhammad |
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Shabir, Muhammad |
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| doi_str |
10.1007/s40314-020-01174-y |
| up_date |
2024-07-04T02:04:30.408Z |
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|
| score |
7.4015865 |