Pythagorean fuzzy multi-criteria decision-making approach based on Spearman rank correlation coefficient
Due to the complexity of objective world, as well as the ambiguity of human thinking, the practical decision-making issues become more and more difficult. Pythagorean fuzzy set is an effective tool for depicting uncertainty of the multi-criteria decision-making problems. This study aims to develop a...
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| Published in: | Soft computing (Berlin, Germany) Vol. 26; no. 6; pp. 3001 - 3012 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Springer Berlin Heidelberg
01.03.2022
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| ISSN: | 1432-7643, 1433-7479 |
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| Abstract | Due to the complexity of objective world, as well as the ambiguity of human thinking, the practical decision-making issues become more and more difficult. Pythagorean fuzzy set is an effective tool for depicting uncertainty of the multi-criteria decision-making problems. This study aims to develop a Pythagorean fuzzy multi-criteria decision-making approach to deal with decision-making problem under uncertainty circumstance. Firstly, the concept, representation and related properties of Spearman rank correlation coefficient (SRCC) originated from statistical theory between two PFSs are introduced, which is used to measure the closeness degree between ideal alternative and each alternative. Then, a multi-criteria decision-making approach with Pythagorean fuzzy environment is developed based on the proposed SRCC. Finally, to illustrate the applicability and effectiveness of the proposed method, a real-world infrastructure project decision-making was demonstrated. The result shows that the main advantage of the proposed decision rule would reduce the complexity of the decision-making problem both in theory and practice. |
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| AbstractList | Due to the complexity of objective world, as well as the ambiguity of human thinking, the practical decision-making issues become more and more difficult. Pythagorean fuzzy set is an effective tool for depicting uncertainty of the multi-criteria decision-making problems. This study aims to develop a Pythagorean fuzzy multi-criteria decision-making approach to deal with decision-making problem under uncertainty circumstance. Firstly, the concept, representation and related properties of Spearman rank correlation coefficient (SRCC) originated from statistical theory between two PFSs are introduced, which is used to measure the closeness degree between ideal alternative and each alternative. Then, a multi-criteria decision-making approach with Pythagorean fuzzy environment is developed based on the proposed SRCC. Finally, to illustrate the applicability and effectiveness of the proposed method, a real-world infrastructure project decision-making was demonstrated. The result shows that the main advantage of the proposed decision rule would reduce the complexity of the decision-making problem both in theory and practice. |
| Author | Su, Limin Li, Huimin Cao, Yongchao |
| Author_xml | – sequence: 1 givenname: Huimin surname: Li fullname: Li, Huimin organization: Department of Construction Engineering and Management, North China University of Water Resources and Electric Power, School of Architecture and Built Environment, Centre for Asian and Middle Eastern Architecture, University of Adelaide – sequence: 2 givenname: Yongchao surname: Cao fullname: Cao, Yongchao organization: School of Management and Economics, North China University of Water Resources and Electric Power, Henan Water Resources Investment and Water and Land Resources Development Co. Ltd – sequence: 3 givenname: Limin orcidid: 0000-0002-9486-711X surname: Su fullname: Su, Limin email: suliminlove2010@163.com organization: School of Mathematics and Statistics, North China University of Water Resources and Electric Power |
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| Keywords | Pythagorean fuzzy set Spearman rank correlation coefficient Decision-making approach Multi-criteria decision-making |
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criteria decision analysisInformation Fusion201841129150 HanafyMSalamaAAMahfouzKMCorrelation coefficients of neutrosophic sets by centroid methodInt J Probab Stat20132912 HungWLWuJWCorrelation of intuitionistic fuzzy sets by centroid methodInf Sci200914421922519301611013.03067 PengXYangYSome results for Pythagorean fuzzy setsInt J Intell Syst20153011331160 PramanikSRoyRRoyTKSmarandacheFMulti criteria decision making using correlation coefficient under rough neutrosophic environmentNeutrosophic Sets Syst2017172936 DikbaşFA new two-dimensional rank correlation coefficientWater Resour Manage201832115 Szmidt E, Kacprzyk J (2010) In The Spearman Rank Correlation Coefficient between Intuitionistic Fuzzy Sets, Proceedings of the 5th IEEE International Conference on Intelligent Systems, London, UK, 2010 GargHGeneralized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multi-criteria decision-making processInt J Intell Syst201732597630 YagerRRPythagorean membership grades in multi-criteria decision makingIEEE Trans Fuzzy Syst201422958965 AczelADComplete business statistics1999McGraw-HillIrwin LiuCTangaGLiubPAn approach to multi-criteria group decision making with unknown weight information based on Pythagorean fuzzy uncertain linguistic aggregation operatorsMath Probl Eng201710.1155/2017/6414020 WangGJLiXPCorrelation and information energy of interval-valued fuzzy numbersFuzzy Sets Syst199910316917516740061017.94034 BustinceHBurilloPCorrelation of interval-valued intuitionistic fuzzy setsFuzzy Sets Syst19957423724413494330875.94156 SuLMWangTZWangLYProject procurement method selection using a multi-criteria decision-making method with interval neutrosophic setsInformation2019106201 GargHPythagorean fuzzy sets and its applications in multi-attribute decision-making processInt J Intell Syst20183312341263 MafakheriFDaiLMSlezakDNasiriFProject delivery system selection under uncertainty: multi-criteria multilevel decision aid modelJ Manag Eng200723200206 WeiGWWangHJLinRApplication of correlation coefficient to interval valued intuitionistic fuzzy multiple attribute decision-making with incomplete weightInf Knowl Inf Syst201126337349 ZhangXXuZExtension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy setsInt J Intell Syst201429106110783379949 ChenHPXuGQYangPLMulti-attribute decision-making approach based on dual hesitant fuzzy information measures and their applicationsMathematics201979786 WanSPJinZDongJYPythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degreesKnowl Inf Syst201855437466 WeiGWLuMTangXYWeiYPythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision makingInt J Intell Syst20183311971233 HongDHFuzzy measures for a correlation coefficient of fuzzy numbers under Tw (the weakest t-norm)-based fuzzy arithmetic operationsInf Sci20061761501601075.03025 GargHA novel correlation coefficients between pythagorean fuzzy sets and its applications to decision-making processesInt J Intell Syst20163112341253 YagerRRAbbasovAMPythagorean membership grades, complex numbers, and decision makingInt J Intell Syst201328436452 YeJFuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environmentEur J Oper Res20102052022041187.90171 RenPXuZGouXPythagorean fuzzy TODIM approach to multi-criteria decision makingAppl Soft Comput201642246259 BonizzoniPVedovaGDDondiRJiangTCorrelation clustering and consensus clusteringLect Notes Comput Sci2008382722623522581041173.68624 YeJMulti-criteria decision-making method using the correlation coefficient under single-valued neutrosophic environmentInt J Gen Syst20134238639430223731278.93240 YeJCorrelation coefficient between dynamic single valued neutrosophic multisets and its multiple attribute decision-making methodInformation2017819 LiHMCaoYCSuLMAn interval Pythagorean fuzzy multi-criteria decision making method based on similarity measures and connection numbersInformation201910280 QuekSGSelvachandranGMunirMMulti-attribute multi-perception decision-making based on generalized T-spherical fuzzy weighted aggregation operators on neutrosophic setsMathematics201979780 RahmanKAbdullahSGeneralized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision-makingGranular Comput20181111 LiangDCDarkoAPXuZSInterval-Valued Pythagorean Fuzzy Extended Bonferroni Mean for Dealing with Heterogenous Relationship among AttributesInt J Intell Syst2018313811411 YeJMulti-criteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval valued intuitionistic fuzzy setsAppl Math Model2010343864387026596401201.91039 Myers JL, Well AW (2003) Research Design and Statistical Analysis (second edition ed.), Lawrence Erlbaum Associates, Mahwah, NJ, 2003 HanafyIMSalamaAAMahfouzKCorrelation of neutrosophic dataJ Eng Sci201213943 KriegelHPKrogerPSchubertEZimekAA General framework for increasing the robustness of PCA-based correlation clustering algorithmsLect Notes Comput Sci20085069418435 GargHA novel accuracy function under interval-valued pythagorean fuzzy environment for solving multi-criteria decision making problemJ Intell Fuzzy Syst2016315295401366.91049 HongDHA note on correlation of interval-valued intuitionistic fuzzy setsFuzzy Sets Syst19989511311716111470924.04002 6615_CR34 S Pramanik (6615_CR28) 2017; 17 M Hanafy (6615_CR15) 2013; 2 GW Wei (6615_CR36) 2018; 33 AD Aczel (6615_CR1) 1999 J Ye (6615_CR44) 2010; 205 IM Hanafy (6615_CR14) 2012; 1 WL Hung (6615_CR18) 2009; 144 J Ye (6615_CR43) 2013; 42 HM Li (6615_CR22) 2019; 10 H Garg (6615_CR8) 2016; 31 DH Hong (6615_CR16) 2006; 176 J Ye (6615_CR45) 2017; 8 SP Wan (6615_CR35) 2018; 55 H Garg (6615_CR10) 2016; 31 HP Kriegel (6615_CR19) 2008; 5069 P Bonizzoni (6615_CR2) 2008; 3827 DG Park (6615_CR26) 2009; 50 RR Yager (6615_CR40) 2013; 28 H Bustince (6615_CR3) 1995; 74 DC Liang (6615_CR20) 2018; 3 H Garg (6615_CR9) 2016; 31 H Garg (6615_CR11) 2017; 32 P Ren (6615_CR31) 2016; 42 GJ Wang (6615_CR39) 1999; 103 DH Hong (6615_CR17) 1998; 95 X Peng (6615_CR27) 2015; 30 RR Yager (6615_CR41) 2014; 22 F Dikbaş (6615_CR7) 2018; 32 6615_CR25 G Wei (6615_CR37) 2017; 27 HP Chen (6615_CR5) 2019; 7 SG Quek (6615_CR29) 2019; 7 H Garg (6615_CR12) 2018; 33 S Broumi (6615_CR4) 2013; 436 TY Chen (6615_CR6) 2018; 41 C Liu (6615_CR23) 2017 T Gerstenkorn (6615_CR13) 1991; 44 X Zhang (6615_CR46) 2014; 29 J Ye (6615_CR42) 2010; 34 D Liang (6615_CR21) 2018; 435 LM Su (6615_CR33) 2019; 10 F Mafakheri (6615_CR24) 2007; 23 K Rahman (6615_CR30) 2018; 1 GW Wei (6615_CR38) 2011; 26 |
| References_xml | – reference: RahmanKAbdullahSGeneralized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision-makingGranular Comput20181111 – reference: GargHA new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision makingInt J Intell Syst201631886920 – reference: Szmidt E, Kacprzyk J (2010) In The Spearman Rank Correlation Coefficient between Intuitionistic Fuzzy Sets, Proceedings of the 5th IEEE International Conference on Intelligent Systems, London, UK, 2010 – reference: YeJCorrelation coefficient between dynamic single valued neutrosophic multisets and its multiple attribute decision-making methodInformation2017819 – reference: HongDHFuzzy measures for a correlation coefficient of fuzzy numbers under Tw (the weakest t-norm)-based fuzzy arithmetic operationsInf Sci20061761501601075.03025 – reference: YagerRRPythagorean membership grades in multi-criteria decision makingIEEE Trans Fuzzy Syst201422958965 – reference: MafakheriFDaiLMSlezakDNasiriFProject delivery system selection under uncertainty: multi-criteria multilevel decision aid modelJ Manag Eng200723200206 – reference: ZhangXXuZExtension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy setsInt J Intell Syst201429106110783379949 – reference: WangGJLiXPCorrelation and information energy of interval-valued fuzzy numbersFuzzy Sets Syst199910316917516740061017.94034 – reference: GargHA novel accuracy function under interval-valued pythagorean fuzzy environment for solving multi-criteria decision making problemJ Intell Fuzzy Syst2016315295401366.91049 – reference: HanafyIMSalamaAAMahfouzKCorrelation of neutrosophic dataJ Eng Sci201213943 – reference: AczelADComplete business statistics1999McGraw-HillIrwin – reference: LiangDXuZLiuDWuYMethod for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy informationInf Sci201843528229537596811440.68292 – reference: BustinceHBurilloPCorrelation of interval-valued intuitionistic fuzzy setsFuzzy Sets Syst19957423724413494330875.94156 – reference: Myers JL, Well AW (2003) Research Design and Statistical Analysis (second edition ed.), Lawrence Erlbaum Associates, Mahwah, NJ, 2003 – reference: GargHGeneralized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multi-criteria decision-making processInt J Intell Syst201732597630 – reference: WeiGWWangHJLinRApplication of correlation coefficient to interval valued intuitionistic fuzzy multiple attribute decision-making with incomplete weightInf Knowl Inf Syst201126337349 – reference: GerstenkornTMankoJCorrelation of intuitionistic fuzzy setsFuzzy Sets and Syst199144394311339810742.04008 – reference: GargHA novel correlation coefficients between pythagorean fuzzy sets and its applications to decision-making processesInt J Intell Syst20163112341253 – reference: PengXYangYSome results for Pythagorean fuzzy setsInt J Intell Syst20153011331160 – reference: HongDHA note on correlation of interval-valued intuitionistic fuzzy setsFuzzy Sets Syst19989511311716111470924.04002 – reference: YeJMulti-criteria decision-making method using the correlation coefficient under single-valued neutrosophic environmentInt J Gen Syst20134238639430223731278.93240 – reference: ChenTYRemoteness index-based pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysisInformation Fusion201841129150 – reference: DikbaşFA new two-dimensional rank correlation coefficientWater Resour Manage201832115 – reference: WanSPJinZDongJYPythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degreesKnowl Inf Syst201855437466 – reference: GargHPythagorean fuzzy sets and its applications in multi-attribute decision-making processInt J Intell Syst20183312341263 – reference: LiHMCaoYCSuLMAn interval Pythagorean fuzzy multi-criteria decision making method based on similarity measures and connection numbersInformation201910280 – reference: ParkDGKwunYCParkJHParkIYCorrelation coefficient of interval valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problemsMath Computer Model2009501279129325834171185.68714 – reference: RenPXuZGouXPythagorean fuzzy TODIM approach to multi-criteria decision makingAppl Soft Comput201642246259 – reference: BonizzoniPVedovaGDDondiRJiangTCorrelation clustering and consensus clusteringLect Notes Comput Sci2008382722623522581041173.68624 – reference: HungWLWuJWCorrelation of intuitionistic fuzzy sets by centroid methodInf Sci200914421922519301611013.03067 – reference: KriegelHPKrogerPSchubertEZimekAA General framework for increasing the robustness of PCA-based correlation clustering algorithmsLect Notes Comput Sci20085069418435 – reference: HanafyMSalamaAAMahfouzKMCorrelation coefficients of neutrosophic sets by centroid methodInt J Probab 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| Title | Pythagorean fuzzy multi-criteria decision-making approach based on Spearman rank correlation coefficient |
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