A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making

Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Py...
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Autor*in:	Muhammad Saeed [verfasserIn] Muhammad Haris Saeed [verfasserIn] Rimsha Shafaqat [verfasserIn] Salvatore Sessa [verfasserIn] Umar Ishtiaq [verfasserIn] Ferdinando di Martino [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	fuzzy set theory soft set decision making distance measures similarity measures

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 14(2022), 12, p 2639
Übergeordnetes Werk:	volume:14 ; year:2022 ; number:12, p 2639

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym14122639

Katalog-ID:	DOAJ082965102

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allfields	10.3390/sym14122639 doi (DE-627)DOAJ082965102 (DE-599)DOAJefa71447bbd349f789d5c5e9409dcef1 DE-627 ger DE-627 rakwb eng QA1-939 Muhammad Saeed verfasserin aut A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<), which are applied in a disease diagnostic decision-making problem. fuzzy set theory soft set decision making distance measures similarity measures Mathematics Muhammad Haris Saeed verfasserin aut Rimsha Shafaqat verfasserin aut Salvatore Sessa verfasserin aut Umar Ishtiaq verfasserin aut Ferdinando di Martino verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 12, p 2639 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:12, p 2639 https://doi.org/10.3390/sym14122639 kostenfrei https://doaj.org/article/efa71447bbd349f789d5c5e9409dcef1 kostenfrei https://www.mdpi.com/2073-8994/14/12/2639 kostenfrei https://doaj.org/toc/2073-8994 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_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 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_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 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 14 2022 12, p 2639
spelling	10.3390/sym14122639 doi (DE-627)DOAJ082965102 (DE-599)DOAJefa71447bbd349f789d5c5e9409dcef1 DE-627 ger DE-627 rakwb eng QA1-939 Muhammad Saeed verfasserin aut A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<), which are applied in a disease diagnostic decision-making problem. fuzzy set theory soft set decision making distance measures similarity measures Mathematics Muhammad Haris Saeed verfasserin aut Rimsha Shafaqat verfasserin aut Salvatore Sessa verfasserin aut Umar Ishtiaq verfasserin aut Ferdinando di Martino verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 12, p 2639 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:12, p 2639 https://doi.org/10.3390/sym14122639 kostenfrei https://doaj.org/article/efa71447bbd349f789d5c5e9409dcef1 kostenfrei https://www.mdpi.com/2073-8994/14/12/2639 kostenfrei https://doaj.org/toc/2073-8994 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_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 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_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 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 14 2022 12, p 2639
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language	English
source	In Symmetry 14(2022), 12, p 2639 volume:14 year:2022 number:12, p 2639
sourceStr	In Symmetry 14(2022), 12, p 2639 volume:14 year:2022 number:12, p 2639
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	fuzzy set theory soft set decision making distance measures similarity measures Mathematics
isfreeaccess_bool	true
container_title	Symmetry
authorswithroles_txt_mv	Muhammad Saeed @@aut@@ Muhammad Haris Saeed @@aut@@ Rimsha Shafaqat @@aut@@ Salvatore Sessa @@aut@@ Umar Ishtiaq @@aut@@ Ferdinando di Martino @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	610604112
id	DOAJ082965102
language_de	englisch
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callnumber-first	Q - Science
author	Muhammad Saeed
spellingShingle	Muhammad Saeed misc QA1-939 misc fuzzy set theory misc soft set misc decision making misc distance measures misc similarity measures misc Mathematics A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making
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topic_title	QA1-939 A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making fuzzy set theory soft set decision making distance measures similarity measures
topic	misc QA1-939 misc fuzzy set theory misc soft set misc decision making misc distance measures misc similarity measures misc Mathematics
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title	A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making
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title_full	A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making
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author_browse	Muhammad Saeed Muhammad Haris Saeed Rimsha Shafaqat Salvatore Sessa Umar Ishtiaq Ferdinando di Martino
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title_sort	theoretical development of cubic pythagorean fuzzy soft set with its application in multi-attribute decision making
callnumber	QA1-939
title_auth	A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making
abstract	Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<), which are applied in a disease diagnostic decision-making problem.
abstractGer	Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<), which are applied in a disease diagnostic decision-making problem.
abstract_unstemmed	Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mi<C</mi<<mrow<<mi<P</mi<<mi<F</mi<<mi<S</mi<<mi<s</mi<</mrow<</msub<</semantics<</math<</inline-formula<), which are applied in a disease diagnostic decision-making problem.
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title_short	A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making
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