An investigation on m-polar fuzzy tolerance graph and its application
Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mahapatra, Tanmoy [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Neural computing & applications - London : Springer, 1993, 34(2021), 4 vom: 06. Okt., Seite 3007-3017 |
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| Übergeordnetes Werk: |
volume:34 ; year:2021 ; number:4 ; day:06 ; month:10 ; pages:3007-3017 |
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| DOI / URN: |
10.1007/s00521-021-06529-y |
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SPR046170472 |
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| 520 | |a Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. | ||
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10.1007/s00521-021-06529-y doi (DE-627)SPR046170472 (SPR)s00521-021-06529-y-e DE-627 ger DE-627 rakwb eng Mahapatra, Tanmoy verfasserin aut An investigation on m-polar fuzzy tolerance graph and its application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. Fuzzy graph (dpeaa)DE-He213 -polar fuzzy graph (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 -polar fuzzy min-tolerance graph (dpeaa)DE-He213 Bounded (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 Pal, Madhumangal (orcid)0000-0002-6709-836X aut Enthalten in Neural computing & applications London : Springer, 1993 34(2021), 4 vom: 06. Okt., Seite 3007-3017 (DE-627)271595574 (DE-600)1480526-1 1433-3058 nnns volume:34 year:2021 number:4 day:06 month:10 pages:3007-3017 https://dx.doi.org/10.1007/s00521-021-06529-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2119 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 AR 34 2021 4 06 10 3007-3017 |
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10.1007/s00521-021-06529-y doi (DE-627)SPR046170472 (SPR)s00521-021-06529-y-e DE-627 ger DE-627 rakwb eng Mahapatra, Tanmoy verfasserin aut An investigation on m-polar fuzzy tolerance graph and its application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. Fuzzy graph (dpeaa)DE-He213 -polar fuzzy graph (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 -polar fuzzy min-tolerance graph (dpeaa)DE-He213 Bounded (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 Pal, Madhumangal (orcid)0000-0002-6709-836X aut Enthalten in Neural computing & applications London : Springer, 1993 34(2021), 4 vom: 06. Okt., Seite 3007-3017 (DE-627)271595574 (DE-600)1480526-1 1433-3058 nnns volume:34 year:2021 number:4 day:06 month:10 pages:3007-3017 https://dx.doi.org/10.1007/s00521-021-06529-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2119 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 AR 34 2021 4 06 10 3007-3017 |
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10.1007/s00521-021-06529-y doi (DE-627)SPR046170472 (SPR)s00521-021-06529-y-e DE-627 ger DE-627 rakwb eng Mahapatra, Tanmoy verfasserin aut An investigation on m-polar fuzzy tolerance graph and its application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. Fuzzy graph (dpeaa)DE-He213 -polar fuzzy graph (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 -polar fuzzy min-tolerance graph (dpeaa)DE-He213 Bounded (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 Pal, Madhumangal (orcid)0000-0002-6709-836X aut Enthalten in Neural computing & applications London : Springer, 1993 34(2021), 4 vom: 06. Okt., Seite 3007-3017 (DE-627)271595574 (DE-600)1480526-1 1433-3058 nnns volume:34 year:2021 number:4 day:06 month:10 pages:3007-3017 https://dx.doi.org/10.1007/s00521-021-06529-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2119 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 AR 34 2021 4 06 10 3007-3017 |
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10.1007/s00521-021-06529-y doi (DE-627)SPR046170472 (SPR)s00521-021-06529-y-e DE-627 ger DE-627 rakwb eng Mahapatra, Tanmoy verfasserin aut An investigation on m-polar fuzzy tolerance graph and its application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. Fuzzy graph (dpeaa)DE-He213 -polar fuzzy graph (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 -polar fuzzy min-tolerance graph (dpeaa)DE-He213 Bounded (dpeaa)DE-He213 -polar fuzzy tolerance graph (dpeaa)DE-He213 Pal, Madhumangal (orcid)0000-0002-6709-836X aut Enthalten in Neural computing & applications London : Springer, 1993 34(2021), 4 vom: 06. Okt., Seite 3007-3017 (DE-627)271595574 (DE-600)1480526-1 1433-3058 nnns volume:34 year:2021 number:4 day:06 month:10 pages:3007-3017 https://dx.doi.org/10.1007/s00521-021-06529-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2119 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 AR 34 2021 4 06 10 3007-3017 |
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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">SPR046170472</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230507102331.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220208s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00521-021-06529-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR046170472</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00521-021-06529-y-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">Mahapatra, Tanmoy</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="3"><subfield code="a">An investigation on m-polar fuzzy tolerance graph and its application</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</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="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. 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An investigation on m-polar fuzzy tolerance graph and its application |
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Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
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Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
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An investigation on m-polar fuzzy tolerance graph and its application |
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| score |
7.402135 |