Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets

The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromo...
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Gespeichert in:

Autor*in:	Wenjuan Ren [verfasserIn] Zhanpeng Yang [verfasserIn] Xipeng Li [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set

Übergeordnetes Werk:	In: Axioms - MDPI AG, 2012, 12(2023), 4, p 376
Übergeordnetes Werk:	volume:12 ; year:2023 ; number:4, p 376

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/axioms12040376

Katalog-ID:	DOAJ089902815

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allfields	10.3390/axioms12040376 doi (DE-627)DOAJ089902815 (DE-599)DOAJ9db81589f5d84eff84a62468a9033888 DE-627 ger DE-627 rakwb eng QA1-939 Wenjuan Ren verfasserin aut Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS. intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set Mathematics Zhanpeng Yang verfasserin aut Xipeng Li verfasserin aut In Axioms MDPI AG, 2012 12(2023), 4, p 376 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:4, p 376 https://doi.org/10.3390/axioms12040376 kostenfrei https://doaj.org/article/9db81589f5d84eff84a62468a9033888 kostenfrei https://www.mdpi.com/2075-1680/12/4/376 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 12 2023 4, p 376
spelling	10.3390/axioms12040376 doi (DE-627)DOAJ089902815 (DE-599)DOAJ9db81589f5d84eff84a62468a9033888 DE-627 ger DE-627 rakwb eng QA1-939 Wenjuan Ren verfasserin aut Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS. intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set Mathematics Zhanpeng Yang verfasserin aut Xipeng Li verfasserin aut In Axioms MDPI AG, 2012 12(2023), 4, p 376 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:4, p 376 https://doi.org/10.3390/axioms12040376 kostenfrei https://doaj.org/article/9db81589f5d84eff84a62468a9033888 kostenfrei https://www.mdpi.com/2075-1680/12/4/376 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 12 2023 4, p 376
allfields_unstemmed	10.3390/axioms12040376 doi (DE-627)DOAJ089902815 (DE-599)DOAJ9db81589f5d84eff84a62468a9033888 DE-627 ger DE-627 rakwb eng QA1-939 Wenjuan Ren verfasserin aut Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS. intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set Mathematics Zhanpeng Yang verfasserin aut Xipeng Li verfasserin aut In Axioms MDPI AG, 2012 12(2023), 4, p 376 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:4, p 376 https://doi.org/10.3390/axioms12040376 kostenfrei https://doaj.org/article/9db81589f5d84eff84a62468a9033888 kostenfrei https://www.mdpi.com/2075-1680/12/4/376 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 12 2023 4, p 376
allfieldsGer	10.3390/axioms12040376 doi (DE-627)DOAJ089902815 (DE-599)DOAJ9db81589f5d84eff84a62468a9033888 DE-627 ger DE-627 rakwb eng QA1-939 Wenjuan Ren verfasserin aut Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS. intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set Mathematics Zhanpeng Yang verfasserin aut Xipeng Li verfasserin aut In Axioms MDPI AG, 2012 12(2023), 4, p 376 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:4, p 376 https://doi.org/10.3390/axioms12040376 kostenfrei https://doaj.org/article/9db81589f5d84eff84a62468a9033888 kostenfrei https://www.mdpi.com/2075-1680/12/4/376 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 12 2023 4, p 376
allfieldsSound	10.3390/axioms12040376 doi (DE-627)DOAJ089902815 (DE-599)DOAJ9db81589f5d84eff84a62468a9033888 DE-627 ger DE-627 rakwb eng QA1-939 Wenjuan Ren verfasserin aut Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS. intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set Mathematics Zhanpeng Yang verfasserin aut Xipeng Li verfasserin aut In Axioms MDPI AG, 2012 12(2023), 4, p 376 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:4, p 376 https://doi.org/10.3390/axioms12040376 kostenfrei https://doaj.org/article/9db81589f5d84eff84a62468a9033888 kostenfrei https://www.mdpi.com/2075-1680/12/4/376 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 12 2023 4, p 376
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source	In Axioms 12(2023), 4, p 376 volume:12 year:2023 number:4, p 376
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callnumber-first	Q - Science
author	Wenjuan Ren
spellingShingle	Wenjuan Ren misc QA1-939 misc intuitionistic fuzzy set misc Gromov–Hausdorff metric information matrix distance misc homogenous metric information matrix misc incomplete intuitionistic fuzzy set misc Mathematics Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets
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topic_title	QA1-939 Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets intuitionistic fuzzy set Gromov–Hausdorff metric information matrix distance homogenous metric information matrix incomplete intuitionistic fuzzy set
topic	misc QA1-939 misc intuitionistic fuzzy set misc Gromov–Hausdorff metric information matrix distance misc homogenous metric information matrix misc incomplete intuitionistic fuzzy set misc Mathematics
topic_unstemmed	misc QA1-939 misc intuitionistic fuzzy set misc Gromov–Hausdorff metric information matrix distance misc homogenous metric information matrix misc incomplete intuitionistic fuzzy set misc Mathematics
topic_browse	misc QA1-939 misc intuitionistic fuzzy set misc Gromov–Hausdorff metric information matrix distance misc homogenous metric information matrix misc incomplete intuitionistic fuzzy set misc Mathematics
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title	Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets
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title_full	Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets
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title_sort	distance measures based on metric information matrix for atanassov’s intuitionistic fuzzy sets
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title_auth	Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets
abstract	The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS.
abstractGer	The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS.
abstract_unstemmed	The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS.
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title_short	Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets
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