Picture fuzzy tolerance graphs with application

Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding...
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Autor*in:	Das, Sankar [verfasserIn] Ghorai, Ganesh Pal, Madhumangal

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Picture fuzzy graphs Picture fuzzy tolerance graphs Picture fuzzy -tolerance graphs Picture fuzzy proper and unit tolerance graphs -tolerance chain graphs

Anmerkung:	© The Author(s) 2021

Übergeordnetes Werk:	Enthalten in: Complex & intelligent systems - Berlin : SpringerOpen, 2015, 8(2021), 1 vom: 30. Sept., Seite 541-554
Übergeordnetes Werk:	volume:8 ; year:2021 ; number:1 ; day:30 ; month:09 ; pages:541-554

Links:	Volltext

DOI / URN:	10.1007/s40747-021-00540-5

Katalog-ID:	SPR046386580

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520			\|a Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs.
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allfields	10.1007/s40747-021-00540-5 doi (DE-627)SPR046386580 (SPR)s40747-021-00540-5-e DE-627 ger DE-627 rakwb eng Das, Sankar verfasserin aut Picture fuzzy tolerance graphs with application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. Picture fuzzy graphs (dpeaa)DE-He213 Picture fuzzy tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance graphs (dpeaa)DE-He213 Picture fuzzy proper and unit tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance chain graphs (dpeaa)DE-He213 Ghorai, Ganesh (orcid)0000-0002-3877-8059 aut Pal, Madhumangal aut Enthalten in Complex & intelligent systems Berlin : SpringerOpen, 2015 8(2021), 1 vom: 30. Sept., Seite 541-554 (DE-627)835589269 (DE-600)2834740-7 2198-6053 nnns volume:8 year:2021 number:1 day:30 month:09 pages:541-554 https://dx.doi.org/10.1007/s40747-021-00540-5 kostenfrei 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2021 1 30 09 541-554
spelling	10.1007/s40747-021-00540-5 doi (DE-627)SPR046386580 (SPR)s40747-021-00540-5-e DE-627 ger DE-627 rakwb eng Das, Sankar verfasserin aut Picture fuzzy tolerance graphs with application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. Picture fuzzy graphs (dpeaa)DE-He213 Picture fuzzy tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance graphs (dpeaa)DE-He213 Picture fuzzy proper and unit tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance chain graphs (dpeaa)DE-He213 Ghorai, Ganesh (orcid)0000-0002-3877-8059 aut Pal, Madhumangal aut Enthalten in Complex & intelligent systems Berlin : SpringerOpen, 2015 8(2021), 1 vom: 30. Sept., Seite 541-554 (DE-627)835589269 (DE-600)2834740-7 2198-6053 nnns volume:8 year:2021 number:1 day:30 month:09 pages:541-554 https://dx.doi.org/10.1007/s40747-021-00540-5 kostenfrei 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2021 1 30 09 541-554
allfields_unstemmed	10.1007/s40747-021-00540-5 doi (DE-627)SPR046386580 (SPR)s40747-021-00540-5-e DE-627 ger DE-627 rakwb eng Das, Sankar verfasserin aut Picture fuzzy tolerance graphs with application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. Picture fuzzy graphs (dpeaa)DE-He213 Picture fuzzy tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance graphs (dpeaa)DE-He213 Picture fuzzy proper and unit tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance chain graphs (dpeaa)DE-He213 Ghorai, Ganesh (orcid)0000-0002-3877-8059 aut Pal, Madhumangal aut Enthalten in Complex & intelligent systems Berlin : SpringerOpen, 2015 8(2021), 1 vom: 30. Sept., Seite 541-554 (DE-627)835589269 (DE-600)2834740-7 2198-6053 nnns volume:8 year:2021 number:1 day:30 month:09 pages:541-554 https://dx.doi.org/10.1007/s40747-021-00540-5 kostenfrei 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2021 1 30 09 541-554
allfieldsGer	10.1007/s40747-021-00540-5 doi (DE-627)SPR046386580 (SPR)s40747-021-00540-5-e DE-627 ger DE-627 rakwb eng Das, Sankar verfasserin aut Picture fuzzy tolerance graphs with application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. Picture fuzzy graphs (dpeaa)DE-He213 Picture fuzzy tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance graphs (dpeaa)DE-He213 Picture fuzzy proper and unit tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance chain graphs (dpeaa)DE-He213 Ghorai, Ganesh (orcid)0000-0002-3877-8059 aut Pal, Madhumangal aut Enthalten in Complex & intelligent systems Berlin : SpringerOpen, 2015 8(2021), 1 vom: 30. Sept., Seite 541-554 (DE-627)835589269 (DE-600)2834740-7 2198-6053 nnns volume:8 year:2021 number:1 day:30 month:09 pages:541-554 https://dx.doi.org/10.1007/s40747-021-00540-5 kostenfrei 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2021 1 30 09 541-554
allfieldsSound	10.1007/s40747-021-00540-5 doi (DE-627)SPR046386580 (SPR)s40747-021-00540-5-e DE-627 ger DE-627 rakwb eng Das, Sankar verfasserin aut Picture fuzzy tolerance graphs with application 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. Picture fuzzy graphs (dpeaa)DE-He213 Picture fuzzy tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance graphs (dpeaa)DE-He213 Picture fuzzy proper and unit tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance chain graphs (dpeaa)DE-He213 Ghorai, Ganesh (orcid)0000-0002-3877-8059 aut Pal, Madhumangal aut Enthalten in Complex & intelligent systems Berlin : SpringerOpen, 2015 8(2021), 1 vom: 30. Sept., Seite 541-554 (DE-627)835589269 (DE-600)2834740-7 2198-6053 nnns volume:8 year:2021 number:1 day:30 month:09 pages:541-554 https://dx.doi.org/10.1007/s40747-021-00540-5 kostenfrei 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2021 1 30 09 541-554
language	English
source	Enthalten in Complex & intelligent systems 8(2021), 1 vom: 30. Sept., Seite 541-554 volume:8 year:2021 number:1 day:30 month:09 pages:541-554
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topic_facet	Picture fuzzy graphs Picture fuzzy tolerance graphs Picture fuzzy -tolerance graphs Picture fuzzy proper and unit tolerance graphs -tolerance chain graphs
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author	Das, Sankar
spellingShingle	Das, Sankar misc Picture fuzzy graphs misc Picture fuzzy tolerance graphs misc Picture fuzzy misc -tolerance graphs misc Picture fuzzy proper and unit tolerance graphs misc -tolerance chain graphs Picture fuzzy tolerance graphs with application
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topic_title	Picture fuzzy tolerance graphs with application Picture fuzzy graphs (dpeaa)DE-He213 Picture fuzzy tolerance graphs (dpeaa)DE-He213 Picture fuzzy (dpeaa)DE-He213 -tolerance graphs (dpeaa)DE-He213 Picture fuzzy proper and unit tolerance graphs (dpeaa)DE-He213 -tolerance chain graphs (dpeaa)DE-He213
topic	misc Picture fuzzy graphs misc Picture fuzzy tolerance graphs misc Picture fuzzy misc -tolerance graphs misc Picture fuzzy proper and unit tolerance graphs misc -tolerance chain graphs
topic_unstemmed	misc Picture fuzzy graphs misc Picture fuzzy tolerance graphs misc Picture fuzzy misc -tolerance graphs misc Picture fuzzy proper and unit tolerance graphs misc -tolerance chain graphs
topic_browse	misc Picture fuzzy graphs misc Picture fuzzy tolerance graphs misc Picture fuzzy misc -tolerance graphs misc Picture fuzzy proper and unit tolerance graphs misc -tolerance chain graphs
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title	Picture fuzzy tolerance graphs with application
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title_sort	picture fuzzy tolerance graphs with application
title_auth	Picture fuzzy tolerance graphs with application
abstract	Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. © The Author(s) 2021
abstractGer	Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. © The Author(s) 2021
abstract_unstemmed	Abstract In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy %$\phi %$-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking %$\phi %$ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy %$\phi %$-tolerance chaingraphs which is the picture fuzzy %$\phi %$-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs. © The Author(s) 2021
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title_short	Picture fuzzy tolerance graphs with application
url	https://dx.doi.org/10.1007/s40747-021-00540-5
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author2	Ghorai, Ganesh Pal, Madhumangal
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