Decision-making model under complex picture fuzzy Hamacher aggregation operators
The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The addition of a neutral membership degree to the definition of CIFS makes CPFS a generalized form of CIFS. The uniqueness of this new theory lies in t...
Saved in:
| Published in | Computational & applied mathematics Vol. 39; no. 3 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.09.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The addition of a neutral membership degree to the definition of CIFS makes CPFS a generalized form of CIFS. The uniqueness of this new theory lies in the capability to attain the wider range with the help of degree of neutral membership, non-membership, and membership. The range of values of membership degrees is broaden to the unit disk in a complex plane. We define elementary operations and properties of CPFSs and explore the MCDM issues with the help of CPFSs, based on Hamacher operations and some aggregation methods. Then, we introduce some operators to aggregate the CPF data, namely complex picture fuzzy Hamacher weighted averaging, ordered weighted averaging, hybrid averaging and complex picture fuzzy Hamacher weighted geometric, ordered weighted geometric and hybrid geometric operators, benefited from the basic Hamacher operations, and averaging, geometric aggregation techniques. We also construct MCDM problem using these operators and perform a calculation for the selection of best ERP system, to demonstrate the authenticity and efficiency of this manuscript. Moreover, we study a comparison to validate the consistency and superiority of our techniques. |
|---|---|
| AbstractList | The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The addition of a neutral membership degree to the definition of CIFS makes CPFS a generalized form of CIFS. The uniqueness of this new theory lies in the capability to attain the wider range with the help of degree of neutral membership, non-membership, and membership. The range of values of membership degrees is broaden to the unit disk in a complex plane. We define elementary operations and properties of CPFSs and explore the MCDM issues with the help of CPFSs, based on Hamacher operations and some aggregation methods. Then, we introduce some operators to aggregate the CPF data, namely complex picture fuzzy Hamacher weighted averaging, ordered weighted averaging, hybrid averaging and complex picture fuzzy Hamacher weighted geometric, ordered weighted geometric and hybrid geometric operators, benefited from the basic Hamacher operations, and averaging, geometric aggregation techniques. We also construct MCDM problem using these operators and perform a calculation for the selection of best ERP system, to demonstrate the authenticity and efficiency of this manuscript. Moreover, we study a comparison to validate the consistency and superiority of our techniques. |
| ArticleNumber | 226 |
| Author | Akram, Muhammad Bashir, Ayesha Garg, Harish |
| Author_xml | – sequence: 1 givenname: Muhammad surname: Akram fullname: Akram, Muhammad organization: Department of Mathematics, University of the Punjab – sequence: 2 givenname: Ayesha surname: Bashir fullname: Bashir, Ayesha organization: Department of Mathematics, University of the Punjab – sequence: 3 givenname: Harish orcidid: 0000-0001-9099-8422 surname: Garg fullname: Garg, Harish email: harish.garg@thapar.edu, harishg58iitr@gmail.com organization: School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University |
| BookMark | eNp9kD1PwzAQhi1UJNrCH2CKxGywz06cjqh8FAkJBpgtx7mElCQOdiLR_nrSFgmJodMN9z73np4ZmbSuRUIuObvmjKmbIJngkjJglHGIOYUTMuUpU5QJBhMyBRApFQkTZ2QWwpoxobiUU_J6h7YKlWtpYz6rtowal2MdDW2OPrKu6Wr8jrrK9oPHqBi22020Mo2xH-PalKXH0vQjHbkOvemdD-fktDB1wIvfOSfvD_dvyxV9fnl8Wt4-Uyv4oqdmbGciNwuwkCDEmUgTqRAyGSu0HHKZYAwo8ixXsSoQCiFtVkCqbKJEYsWcXB3udt59DRh6vXaDb8dKDRKkimUqYUylh5T1LgSPhbZVv_-496aqNWd6508f_OnRn9770zsU_qGdrxrjN8chcYDCGG5L9H9fHaF-AFn6hPo |
| CitedBy_id | crossref_primary_10_1155_2021_8873230 crossref_primary_10_1016_j_aej_2023_11_079 crossref_primary_10_1155_2021_6628745 crossref_primary_10_2298_YJOR240218030A crossref_primary_10_1109_ACCESS_2021_3110273 crossref_primary_10_1038_s41598_024_82532_2 crossref_primary_10_1016_j_engappai_2024_108154 crossref_primary_10_3233_JIFS_211455 crossref_primary_10_1155_2022_1651017 crossref_primary_10_3390_math8101647 crossref_primary_10_1007_s40815_022_01262_7 crossref_primary_10_2139_ssrn_4183223 crossref_primary_10_1007_s13369_020_05313_9 crossref_primary_10_26599_FIE_2024_9270048 crossref_primary_10_1016_j_heliyon_2023_e17278 crossref_primary_10_1038_s41598_024_54422_0 crossref_primary_10_1109_ACCESS_2023_3308030 crossref_primary_10_1007_s44196_024_00504_w crossref_primary_10_1155_2021_9427492 crossref_primary_10_3233_JIFS_201385 crossref_primary_10_1155_2022_7254306 crossref_primary_10_1155_2022_6518976 crossref_primary_10_1007_s40747_022_00959_4 crossref_primary_10_1109_ACCESS_2023_3313181 crossref_primary_10_1007_s40747_024_01372_9 crossref_primary_10_1016_j_inffus_2022_11_009 crossref_primary_10_1088_1402_4896_ac7980 crossref_primary_10_3390_sym15030595 crossref_primary_10_1016_j_orp_2022_100251 crossref_primary_10_1109_ACCESS_2024_3519792 crossref_primary_10_1016_j_eswa_2022_119331 crossref_primary_10_1007_s41066_021_00256_4 crossref_primary_10_1016_j_engappai_2024_107996 crossref_primary_10_1155_2020_3263407 crossref_primary_10_3934_jimo_2020162 crossref_primary_10_1007_s12190_024_02293_z crossref_primary_10_1109_ACCESS_2023_3285307 crossref_primary_10_1155_2022_6269115 crossref_primary_10_1016_j_aej_2023_06_064 crossref_primary_10_1016_j_ins_2024_120101 crossref_primary_10_1016_j_scs_2024_105842 crossref_primary_10_1155_2022_2880340 crossref_primary_10_3233_JIFS_221768 crossref_primary_10_1007_s11277_024_11573_7 crossref_primary_10_1007_s41066_021_00282_2 crossref_primary_10_3934_math_20241321 crossref_primary_10_1007_s40314_021_01699_w crossref_primary_10_3233_JIFS_232529 crossref_primary_10_1109_ACCESS_2024_3359904 crossref_primary_10_1155_2022_1460544 crossref_primary_10_1016_j_engappai_2024_109650 crossref_primary_10_1007_s12559_022_10100_9 crossref_primary_10_3390_sym15030577 crossref_primary_10_1016_j_heliyon_2024_e32897 crossref_primary_10_1155_2021_6644994 crossref_primary_10_35378_gujs_937205 crossref_primary_10_3390_sym15030651 crossref_primary_10_1007_s40314_024_03035_4 crossref_primary_10_1109_ACCESS_2024_3397854 crossref_primary_10_1371_journal_pone_0273642 crossref_primary_10_1016_j_heliyon_2024_e25368 crossref_primary_10_1038_s41598_024_73488_4 crossref_primary_10_1007_s40314_022_01837_y crossref_primary_10_1016_j_engappai_2024_109169 crossref_primary_10_3390_sym17010034 crossref_primary_10_1038_s41598_024_65679_w crossref_primary_10_3233_JIFS_201611 crossref_primary_10_1155_2021_9937828 crossref_primary_10_1016_j_ins_2023_119163 crossref_primary_10_1155_2022_7389882 crossref_primary_10_1371_journal_pone_0305319 crossref_primary_10_3390_math12132086 crossref_primary_10_3390_sym15010251 crossref_primary_10_1007_s11042_023_17723_6 crossref_primary_10_3390_sym15040861 crossref_primary_10_1016_j_rineng_2024_103867 crossref_primary_10_1016_j_asoc_2023_110088 crossref_primary_10_1007_s40747_023_01217_x crossref_primary_10_1016_j_asoc_2024_112526 crossref_primary_10_1007_s41066_022_00350_1 crossref_primary_10_1155_2021_5556017 crossref_primary_10_1109_ACCESS_2024_3412755 crossref_primary_10_1142_S2661335224500126 crossref_primary_10_1007_s44196_021_00038_5 crossref_primary_10_1155_2022_1476233 crossref_primary_10_3390_electronics11233841 crossref_primary_10_1016_j_eswa_2021_114597 crossref_primary_10_1155_2023_3516707 crossref_primary_10_1007_s00500_021_06108_2 crossref_primary_10_3233_JIFS_202000 crossref_primary_10_1016_j_asoc_2024_111308 crossref_primary_10_1038_s41598_022_20239_y crossref_primary_10_1109_ACCESS_2024_3490652 crossref_primary_10_1142_S2972370124500089 crossref_primary_10_3390_su16073069 crossref_primary_10_52280_pujm_2021_530701 crossref_primary_10_1111_exsy_12712 crossref_primary_10_1155_2022_3304333 crossref_primary_10_1002_mma_8551 crossref_primary_10_1016_j_matpr_2021_12_117 crossref_primary_10_1016_j_asoc_2024_111532 crossref_primary_10_3233_JIFS_200194 crossref_primary_10_1007_s12652_021_03370_y crossref_primary_10_3390_math8101653 crossref_primary_10_1002_int_22618 |
| Cites_doi | 10.1007/s41066-020-00213-7 10.1007/s41066-020-00223-5 10.1007/s13369-017-2625-9 10.1016/S0165-0114(86)80034-3 10.1109/21.87068 10.1002/int.22183 10.3390/sym11111381 10.3233/JIFS-161798 10.1109/TFUZZ.2012.2189405 10.1007/s40096-019-0291-7 10.1002/int.22103 10.1615/Int.J.UncertaintyQuantification.2017020356 10.1016/j.ejor.2006.04.009 10.1007/s13369-018-3532-4 10.1109/TFUZZ.2003.814832 10.3390/sym11101313 10.1109/TFUZZ.2003.822678 10.1111/exsy.12325 10.1109/TFUZZ.2019.2897961 10.1109/TFUZZ.2006.890678 10.3233/JIFS-200789 10.1016/j.ijar.2009.05.010 10.3390/sym11121498 10.1016/j.is.2006.10.005 10.1016/j.ins.2005.07.006 10.1016/0165-0114(94)90084-1 10.3233/IFS-131019 10.1016/S0019-9958(65)90241-X 10.1063/1.4757515 10.1007/s13369-018-3413-x 10.1007/s10489-017-0930-3 10.1109/91.995119 10.1016/j.omega.2005.12.003 10.1016/S0888-613X(98)10018-X 10.1109/ACCESS.2018.2832206 10.1109/TFUZZ.2013.2278989 10.3390/math8010070 10.3390/a12110234 10.1109/WICT.2013.7113099 10.1016/j.cie.2016.08.017 10.1080/03081070600574353 |
| ContentType | Journal Article |
| Copyright | SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020. |
| Copyright_xml | – notice: SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 – notice: SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s40314-020-01251-2 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1807-0302 |
| ExternalDocumentID | 10_1007_s40314_020_01251_2 |
| GroupedDBID | -EM .4S .DC 06D 0R~ 203 29F 2WC 30V 4.4 406 5GY 69Q 96X AAAVM AACDK AAHNG AAIAL AAJBT AAJKR AAKPC AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAZMS ABAKF ABDZT ABECU ABFTV ABJNI ABJOX ABKCH ABMQK ABQBU ABTEG ABTHY ABTKH ABTMW ABXHO ABXPI ACAOD ACCUX ACDTI ACGFO ACGFS ACHSB ACIPV ACIWK ACKNC ACMLO ACOKC ACPIV ACREN ACZOJ ADBBV ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFQL AEGNC AEGXH AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETCA AEVLU AEXYK AFBBN AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AIAGR AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKLTO ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMTXH AMXSW AMYLF AMYQR ANMIH APOWU ARCSS ASPBG AUKKA AVWKF AXYYD AYJHY AZFZN BAPOH BGNMA C1A CS3 CSCUP DNIVK DPUIP DU5 E3Z EBLON EBS EDO EIOEI EJD ESBYG FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FYJPI GGCAI GGRSB GJIRD GQ7 HMJXF HRMNR HZ~ I0C IKXTQ IWAJR IXD J-C JBSCW JZLTJ KOV KQ8 KWQ LLZTM M4Y M~E NPVJJ NQJWS NU0 O9- O93 O9G O9J OK1 P2P PT4 RLLFE RNS ROL RSC RSV SCD SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE TR2 TSG UG4 UOJIU UTJUX UZXMN VFIZW W48 XSB Z7R Z83 ZMTXR AAYXX ABBRH ABDBE ABFSG ACMFV ACSTC AEZWR AFDZB AFHIU AFOHR AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION OVT ABRTQ |
| ID | FETCH-LOGICAL-c319t-a14403da92c26e25b38647e2b457ec12d46e52e3dbd757fe2f34cbf287c6736c3 |
| IEDL.DBID | AGYKE |
| ISSN | 2238-3603 |
| IngestDate | Fri Jul 25 11:10:09 EDT 2025 Tue Jul 01 00:46:03 EDT 2025 Thu Apr 24 23:10:29 EDT 2025 Fri Feb 21 02:28:02 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Averaging operators 03E72 Geometric operators 47S40 Complex picture fuzzy set Hamacher operations |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-a14403da92c26e25b38647e2b457ec12d46e52e3dbd757fe2f34cbf287c6736c3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-9099-8422 |
| PQID | 2424754842 |
| PQPubID | 2044245 |
| ParticipantIDs | proquest_journals_2424754842 crossref_citationtrail_10_1007_s40314_020_01251_2 crossref_primary_10_1007_s40314_020_01251_2 springer_journals_10_1007_s40314_020_01251_2 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20200900 |
| PublicationDateYYYYMMDD | 2020-09-01 |
| PublicationDate_xml | – month: 9 year: 2020 text: 20200900 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Heidelberg |
| PublicationTitle | Computational & applied mathematics |
| PublicationTitleAbbrev | Comp. Appl. Math |
| PublicationYear | 2020 |
| Publisher | Springer International Publishing Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer Nature B.V |
| References | Roychowdhury, Wang (CR37) 1998; 19 Garg (CR18) 2017; 42 Zhang, Dillon, Cai, Ma, Lu (CR52) 2009; 50 CR36 Beliakov, Pradera, Calvo (CR8) 2007 Garg, Kaur (CR19) 2019; 33 Liao, Li, Lu (CR27) 2007; 32 Shahzadi, Akram, Al-Kenani (CR38) 2020; 8 Akram, Garg, Zahid (CR5) 2020; 17 Wang, Triantaphyllou (CR41) 2008; 36 Ye (CR50) 2017; 47 Luqman, Akram, Smarandache (CR31) 2019; 12 Deschrijver, Cornelis, Kerre (CR14) 2004; 12 Shumaiza, Akram, Alcantud (CR39) 2019; 11 CR6 Figueira, Greco, Ehrgott (CR16) 2016 Akram, Dudek, Ilyas (CR4) 2019; 34 Xu (CR46) 2007; 15 Yager (CR48) 1988; 18 Huang (CR24) 2014; 27 Fan, Song, Fu, Lei, Wang (CR15) 2018; 6 Akram, Dudek, Dar (CR3) 2019; 34 Garg, Rani (CR21) 2019; 44 Wang, Liu (CR40) 2012; 20 Wu, Wei (CR45) 2017; 21 CR11 CR10 Wei (CR44) 2018; 157 Wei (CR43) 2017; 33 Cuong (CR12) 2013 Rani, Garg (CR35) 2017; 7 Chen, Tan (CR9) 1994; 167 Ramot, Milo, Friedman, Kandel (CR33) 2002; 10 Yager (CR49) 2013; 22 Deschrijver, Kerre (CR13) 2002; 8 CR29 Zadeh (CR51) 1965; 8 Garg, Kumar (CR20) 2019; 27 Liu, Wang (CR28) 2007; 179 CR23 Garg (CR17) 2016; 101 CR22 Akram, Khan (CR2) 2020 Ramot, Friedman, Langholz, Kandel (CR34) 2003; 11 Kaur, Garg (CR25) 2019; 44 Xu, Yager (CR47) 2006; 35 Pasi, Yager (CR32) 2006; 176 Akram, Bashir (CR1) 2020 Waseem, Akram, Alcantud (CR42) 2019; 11 Luqman, Akram, Al-Kenani, Alcantud (CR30) 2019; 11 Atanassov (CR7) 1986; 20 Khan, Abdullah, Ashraf (CR26) 2019; 13 K Atanassov (1251_CR7) 1986; 20 1251_CR6 H Garg (1251_CR18) 2017; 42 H Garg (1251_CR20) 2019; 27 X Liao (1251_CR27) 2007; 32 D Ramot (1251_CR33) 2002; 10 LA Zadeh (1251_CR51) 1965; 8 G Pasi (1251_CR32) 2006; 176 W Wang (1251_CR40) 2012; 20 H Garg (1251_CR17) 2016; 101 M Akram (1251_CR1) 2020 N Waseem (1251_CR42) 2019; 11 G Kaur (1251_CR25) 2019; 44 1251_CR36 G Deschrijver (1251_CR14) 2004; 12 SJ Wu (1251_CR45) 2017; 21 ZS Xu (1251_CR47) 2006; 35 M Shumaiza (1251_CR39) 2019; 11 M Akram (1251_CR3) 2019; 34 A Luqman (1251_CR30) 2019; 11 GT Zhang (1251_CR52) 2009; 50 D Rani (1251_CR35) 2017; 7 1251_CR23 1251_CR22 ZS Xu (1251_CR46) 2007; 15 A Luqman (1251_CR31) 2019; 12 M Akram (1251_CR4) 2019; 34 M Akram (1251_CR5) 2020; 17 1251_CR29 RR Yager (1251_CR49) 2013; 22 S Khan (1251_CR26) 2019; 13 S Roychowdhury (1251_CR37) 1998; 19 J Figueira (1251_CR16) 2016 RR Yager (1251_CR48) 1988; 18 J Ye (1251_CR50) 2017; 47 SM Chen (1251_CR9) 1994; 167 D Ramot (1251_CR34) 2003; 11 CL Fan (1251_CR15) 2018; 6 GW Wei (1251_CR43) 2017; 33 1251_CR10 1251_CR11 G Deschrijver (1251_CR13) 2002; 8 HW Liu (1251_CR28) 2007; 179 H Garg (1251_CR19) 2019; 33 H Garg (1251_CR21) 2019; 44 G Beliakov (1251_CR8) 2007 G Wei (1251_CR44) 2018; 157 G Shahzadi (1251_CR38) 2020; 8 M Akram (1251_CR2) 2020 B Cuong (1251_CR12) 2013 JY Huang (1251_CR24) 2014; 27 X Wang (1251_CR41) 2008; 36 |
| References_xml | – volume: 101 start-page: 53 year: 2016 end-page: 69 ident: CR17 article-title: Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein tnorm and t-conorm and their application to decision making publication-title: Comput Ind Eng – ident: CR22 – year: 2020 ident: CR1 article-title: Complex fuzzy ordered weighted quadratic averaging operators publication-title: Granul Comput doi: 10.1007/s41066-020-00213-7 – volume: 11 start-page: 1498 issue: 12 year: 2019 ident: CR42 article-title: Multi-attribute decision-making based on m-polar fuzzy Hamacher aggregation operators publication-title: Symmetry – volume: 157 start-page: 271 issue: 3 year: 2018 end-page: 320 ident: CR44 article-title: Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making publication-title: Fund Inform – volume: 21 start-page: 189 issue: 3 year: 2017 end-page: 201 ident: CR45 article-title: Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making publication-title: Int J Knowl Based Intell Eng Syst – ident: CR29 – volume: 44 start-page: 2775 issue: 3 year: 2019 end-page: 2794 ident: CR25 article-title: Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process publication-title: Arab J Sci Eng – volume: 32 start-page: 1005 issue: 7 year: 2007 end-page: 1017 ident: CR27 article-title: A model for selecting an ERP system based on linguistic information processing publication-title: Inform Syst – volume: 7 start-page: 423 issue: 5 year: 2017 end-page: 439 ident: CR35 article-title: Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process publication-title: Int J Uncert Quantif – volume: 47 start-page: 743 year: 2017 end-page: 751 ident: CR50 article-title: Intuitionistic fuzzy hybrid arithmetic and geometric aggregation operators for the decision-making of mechanical design schemes publication-title: Appl Intell – volume: 36 start-page: 45 year: 2008 end-page: 63 ident: CR41 article-title: Ranking irregularities when evaluating alternatives by using some ELECTRE methods publication-title: Omega – volume: 34 start-page: 1455 year: 2019 end-page: 1475 ident: CR4 article-title: Group decision making based on Pythagorean fuzzy TOPSIS method publication-title: Int J Intell Syst – volume: 19 start-page: 419 issue: 3–4 year: 1998 end-page: 439 ident: CR37 article-title: On generalized Hamacher families of triangular operators publication-title: Int J Approx Reason – ident: CR11 – volume: 8 start-page: 19 year: 2002 end-page: 27 ident: CR13 article-title: A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms publication-title: Notes Intuit Fuzzy Sets – volume: 10 start-page: 171 issue: 2 year: 2002 end-page: 186 ident: CR33 article-title: Complex fuzzy sets publication-title: IEEE Trans Fuzzy Syst – volume: 35 start-page: 417 year: 2006 end-page: 433 ident: CR47 article-title: Some geometric aggregation operators based on intuitionistic fuzzy sets publication-title: Int J Gen Syst – ident: CR36 – volume: 11 start-page: 1313 issue: 10 year: 2019 ident: CR39 article-title: Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information publication-title: Symmetry – volume: 11 start-page: 450 issue: 4 year: 2003 end-page: 461 ident: CR34 article-title: Complex fuzzy logic publication-title: IEEE Transa Fuzzy Syst – volume: 42 start-page: 5275 issue: 12 year: 2017 end-page: 5290 ident: CR18 article-title: Some picture fuzzy aggregation operators and their applications to multicriteria decision-making publication-title: Arab J Sci Eng – volume: 33 start-page: 713 issue: 2 year: 2017 end-page: 724 ident: CR43 article-title: Picture fuzzy aggregation operators and their application to multiple attribute decision making publication-title: J Intell Fuzzy Syst – volume: 176 start-page: 390 year: 2006 end-page: 414 ident: CR32 article-title: Modelling the concept of majority opinion in group decision making publication-title: Inform Sci – volume: 33 start-page: 507 issue: 6 year: 2019 end-page: 537 ident: CR19 article-title: Cubic intuitionistic fuzzy sets and its fundamental properties publication-title: J Mult Valued Logic Soft Comput – volume: 8 start-page: 338 issue: 3 year: 1965 end-page: 356 ident: CR51 article-title: Fuzzy sets publication-title: Inform Control – volume: 27 start-page: 2302 issue: 12 year: 2019 end-page: 2311 ident: CR20 article-title: Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems publication-title: IEEE Transa Fuzzy Syst – volume: 6 start-page: 27214 year: 2018 end-page: 27238 ident: CR15 article-title: New operators for aggregating intuitionistic fuzzy information with their application in decision making publication-title: IEEE Access – ident: CR10 – volume: 20 start-page: 923 issue: 5 year: 2012 end-page: 938 ident: CR40 article-title: Intuitionistic fuzzy information aggregation using Einstein operations publication-title: IEEE Transa Fuzzy Syst – year: 2020 ident: CR2 article-title: Complex Pythagorean Dombi fuzzy graphs for decision making publication-title: Granul Comput doi: 10.1007/s41066-020-00223-5 – volume: 34 start-page: 3000 year: 2019 end-page: 3019 ident: CR3 article-title: Pythagorean dombi fuzzy aggregation operators with application in multi-criteria decision-making publication-title: Int J Intell Syst – volume: 167 start-page: 163 year: 1994 end-page: 172 ident: CR9 article-title: Handling multicriteria fuzzy decision-making problems based on vague set theory publication-title: Fuzzy Sets Syst – ident: CR6 – volume: 13 start-page: 213 issue: 3 year: 2019 end-page: 229 ident: CR26 article-title: Picture fuzzy aggregation information based on Einstein operations and their application in decision making publication-title: Math Sci – volume: 15 start-page: 1179 issue: 6 year: 2007 end-page: 1187 ident: CR46 article-title: Intuitionistic fuzzy aggregation operators publication-title: IEEE Trans Fuzzy Syst – volume: 12 start-page: 45 issue: 1 year: 2004 end-page: 61 ident: CR14 article-title: On the representation of intuitionistic fuzzy t-norms and t-conorms publication-title: IEEE Trans Fuzzy Syst – year: 2016 ident: CR16 publication-title: Multiple criteria decision analysis – volume: 8 start-page: 70 issue: 1 year: 2020 ident: CR38 article-title: Decision-making approach under Pythagorean fuzzy Yager weighted operators publication-title: Mathematics – volume: 17 start-page: 147 issue: 5 year: 2020 end-page: 164 ident: CR5 article-title: Extensions of ELECTRE-I and TOPSIS methods for group decision-making under complex Pythagorean fuzzy environment publication-title: Iran J Fuzzy Syst – year: 2013 ident: CR12 publication-title: Picture fuzzy sets-first results. Neuro-Fuzzy systems with applications – ident: CR23 – volume: 179 start-page: 220 issue: 1 year: 2007 end-page: 233 ident: CR28 article-title: Multi-criteria decision-making methods based on intuitionistic fuzzy sets publication-title: Eur J Oper Res – volume: 11 start-page: 1381 issue: 11 year: 2019 ident: CR30 article-title: A study on hypergraph representations of complex fuzzy information publication-title: Symmetry – volume: 12 start-page: 234 issue: 11 year: 2019 ident: CR31 article-title: Complex neutrosophic hypergraphs: new social network models publication-title: Algorithms – volume: 18 start-page: 183 issue: 1 year: 1988 end-page: 190 ident: CR48 article-title: On ordered weighted averaging aggregation operators in multicriteria decision making publication-title: IEEE Trans Syst Man Cybern – volume: 27 start-page: 505 year: 2014 end-page: 513 ident: CR24 article-title: Intuitionistic fuzzy Hamacher aggregation operator and their application tomultiple attribute decision making publication-title: J Intell Fuzzy Syst – volume: 20 start-page: 87 issue: 1 year: 1986 end-page: 96 ident: CR7 article-title: Intuitionistic fuzzy sets publication-title: Fuzzy Sets Syst – volume: 44 start-page: 2679 issue: 3 year: 2019 end-page: 2698 ident: CR21 article-title: Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process publication-title: Arabi J Sci Eng – volume: 50 start-page: 1227 year: 2009 end-page: 1249 ident: CR52 article-title: Operation properties and -equalities of complex fuzzy sets publication-title: Int J Approx Reason – year: 2007 ident: CR8 publication-title: Aggregation functions. A guide for practitioners – volume: 22 start-page: 958 issue: 4 year: 2013 end-page: 965 ident: CR49 article-title: Pythagorean membership grades in multicriteria decision making publication-title: IEEE Trans Fuzzy Syst – volume: 42 start-page: 5275 issue: 12 year: 2017 ident: 1251_CR18 publication-title: Arab J Sci Eng doi: 10.1007/s13369-017-2625-9 – volume: 20 start-page: 87 issue: 1 year: 1986 ident: 1251_CR7 publication-title: Fuzzy Sets Syst doi: 10.1016/S0165-0114(86)80034-3 – volume: 18 start-page: 183 issue: 1 year: 1988 ident: 1251_CR48 publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/21.87068 – volume-title: Aggregation functions. A guide for practitioners year: 2007 ident: 1251_CR8 – volume: 21 start-page: 189 issue: 3 year: 2017 ident: 1251_CR45 publication-title: Int J Knowl Based Intell Eng Syst – volume: 34 start-page: 3000 year: 2019 ident: 1251_CR3 publication-title: Int J Intell Syst doi: 10.1002/int.22183 – volume-title: Multiple criteria decision analysis year: 2016 ident: 1251_CR16 – volume: 8 start-page: 19 year: 2002 ident: 1251_CR13 publication-title: Notes Intuit Fuzzy Sets – ident: 1251_CR10 – volume: 11 start-page: 1381 issue: 11 year: 2019 ident: 1251_CR30 publication-title: Symmetry doi: 10.3390/sym11111381 – volume: 33 start-page: 713 issue: 2 year: 2017 ident: 1251_CR43 publication-title: J Intell Fuzzy Syst doi: 10.3233/JIFS-161798 – volume: 20 start-page: 923 issue: 5 year: 2012 ident: 1251_CR40 publication-title: IEEE Transa Fuzzy Syst doi: 10.1109/TFUZZ.2012.2189405 – volume: 17 start-page: 147 issue: 5 year: 2020 ident: 1251_CR5 publication-title: Iran J Fuzzy Syst – volume: 13 start-page: 213 issue: 3 year: 2019 ident: 1251_CR26 publication-title: Math Sci doi: 10.1007/s40096-019-0291-7 – volume: 34 start-page: 1455 year: 2019 ident: 1251_CR4 publication-title: Int J Intell Syst doi: 10.1002/int.22103 – volume: 7 start-page: 423 issue: 5 year: 2017 ident: 1251_CR35 publication-title: Int J Uncert Quantif doi: 10.1615/Int.J.UncertaintyQuantification.2017020356 – volume: 179 start-page: 220 issue: 1 year: 2007 ident: 1251_CR28 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2006.04.009 – volume: 44 start-page: 2775 issue: 3 year: 2019 ident: 1251_CR25 publication-title: Arab J Sci Eng doi: 10.1007/s13369-018-3532-4 – volume: 11 start-page: 450 issue: 4 year: 2003 ident: 1251_CR34 publication-title: IEEE Transa Fuzzy Syst doi: 10.1109/TFUZZ.2003.814832 – volume: 11 start-page: 1313 issue: 10 year: 2019 ident: 1251_CR39 publication-title: Symmetry doi: 10.3390/sym11101313 – volume: 12 start-page: 45 issue: 1 year: 2004 ident: 1251_CR14 publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2003.822678 – ident: 1251_CR36 doi: 10.1111/exsy.12325 – volume: 27 start-page: 2302 issue: 12 year: 2019 ident: 1251_CR20 publication-title: IEEE Transa Fuzzy Syst doi: 10.1109/TFUZZ.2019.2897961 – volume: 15 start-page: 1179 issue: 6 year: 2007 ident: 1251_CR46 publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2006.890678 – volume: 33 start-page: 507 issue: 6 year: 2019 ident: 1251_CR19 publication-title: J Mult Valued Logic Soft Comput – ident: 1251_CR29 doi: 10.3233/JIFS-200789 – volume: 50 start-page: 1227 year: 2009 ident: 1251_CR52 publication-title: Int J Approx Reason doi: 10.1016/j.ijar.2009.05.010 – volume: 11 start-page: 1498 issue: 12 year: 2019 ident: 1251_CR42 publication-title: Symmetry doi: 10.3390/sym11121498 – volume: 32 start-page: 1005 issue: 7 year: 2007 ident: 1251_CR27 publication-title: Inform Syst doi: 10.1016/j.is.2006.10.005 – volume: 176 start-page: 390 year: 2006 ident: 1251_CR32 publication-title: Inform Sci doi: 10.1016/j.ins.2005.07.006 – volume: 167 start-page: 163 year: 1994 ident: 1251_CR9 publication-title: Fuzzy Sets Syst doi: 10.1016/0165-0114(94)90084-1 – volume: 27 start-page: 505 year: 2014 ident: 1251_CR24 publication-title: J Intell Fuzzy Syst doi: 10.3233/IFS-131019 – volume: 157 start-page: 271 issue: 3 year: 2018 ident: 1251_CR44 publication-title: Fund Inform – volume-title: Picture fuzzy sets-first results. Neuro-Fuzzy systems with applications year: 2013 ident: 1251_CR12 – volume: 8 start-page: 338 issue: 3 year: 1965 ident: 1251_CR51 publication-title: Inform Control doi: 10.1016/S0019-9958(65)90241-X – ident: 1251_CR6 doi: 10.1063/1.4757515 – ident: 1251_CR23 – volume: 44 start-page: 2679 issue: 3 year: 2019 ident: 1251_CR21 publication-title: Arabi J Sci Eng doi: 10.1007/s13369-018-3413-x – volume: 47 start-page: 743 year: 2017 ident: 1251_CR50 publication-title: Appl Intell doi: 10.1007/s10489-017-0930-3 – volume: 10 start-page: 171 issue: 2 year: 2002 ident: 1251_CR33 publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/91.995119 – volume: 36 start-page: 45 year: 2008 ident: 1251_CR41 publication-title: Omega doi: 10.1016/j.omega.2005.12.003 – volume: 19 start-page: 419 issue: 3–4 year: 1998 ident: 1251_CR37 publication-title: Int J Approx Reason doi: 10.1016/S0888-613X(98)10018-X – volume: 6 start-page: 27214 year: 2018 ident: 1251_CR15 publication-title: IEEE Access doi: 10.1109/ACCESS.2018.2832206 – volume: 22 start-page: 958 issue: 4 year: 2013 ident: 1251_CR49 publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2013.2278989 – volume: 8 start-page: 70 issue: 1 year: 2020 ident: 1251_CR38 publication-title: Mathematics doi: 10.3390/math8010070 – year: 2020 ident: 1251_CR2 publication-title: Granul Comput doi: 10.1007/s41066-020-00223-5 – volume: 12 start-page: 234 issue: 11 year: 2019 ident: 1251_CR31 publication-title: Algorithms doi: 10.3390/a12110234 – ident: 1251_CR22 – ident: 1251_CR11 doi: 10.1109/WICT.2013.7113099 – volume: 101 start-page: 53 year: 2016 ident: 1251_CR17 publication-title: Comput Ind Eng doi: 10.1016/j.cie.2016.08.017 – volume: 35 start-page: 417 year: 2006 ident: 1251_CR47 publication-title: Int J Gen Syst doi: 10.1080/03081070600574353 – year: 2020 ident: 1251_CR1 publication-title: Granul Comput doi: 10.1007/s41066-020-00213-7 |
| SSID | ssj0037144 |
| Score | 2.485201 |
| Snippet | The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| SubjectTerms | Agglomeration Applications of Mathematics Applied physics Computational mathematics Computational Mathematics and Numerical Analysis Decision making Fuzzy sets Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Operators |
| Title | Decision-making model under complex picture fuzzy Hamacher aggregation operators |
| URI | https://link.springer.com/article/10.1007/s40314-020-01251-2 https://www.proquest.com/docview/2424754842 |
| Volume | 39 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LTwIxEG4MXPQgihpRJD140xLodh8cQUGigXiQBE-bttslRnmEhUT59U5Ld4lETTi323Q70858mZlvELp2PHgWladp9gGrMuG5JOBKEeaxGNBBIH2qC5x7fa87YI9Dd2iLwpI02z0NSZqXOit2Y5ppnWi4U9NWmcDDmwf_o-bmUL758PrUTl9gTUKno8lg-QKiN2OLZX5f5adB2niZW4FRY286BTRId7pOM3mvLheiKldbJI67_soROrQOKG6uNeYY7alJERWsM4rtVU-K6KCXEbomJ-j53vbiIWPTvgqbDjpYV6DNsUlLV5949mbiETherlZfuMvHhiwa8xFg-pHRADydKRPXT07RoNN-uesS24yBSLilC8J1FNiJeINK6inqCifwmK-oYK6vZJ1GzFMuVU4kIt_1Y0Vjh0kRAyCTOnVMOmcoN5lO1DnCDRdQaQxQioNtBHdD1COQlCaeB0PJG7yE6qlEQmmZynXDjI8w41g2BxjCAYbmAENaQjfZN7M1T8e_s8upoEN7Z5NQF8r4AOAYDN-mctsM_73axW7TL9E-NaLXiWpllFvMl-oKPJuFqIAid1qtfsUq9DcOtew2 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwzV1LTwIxEJ4oHNSD-Iwoag960hLpdnfh4IH4QhHjQRM9rbvdLjHKIyxE4ff4V_xfTksXolETDySe22227XRmvszMNwA7loNqUTqKZh-xKg8cmxZ9KSl3eITooChcpgqca1dO5ZZf3Nl3U_CW1MLobPckJKk19ajYjSumdargzoGyypSZVMqq7L8gUIsPz4_xVncZOz25OapQ00uAChSyLvVVENMK_RITzJHMDqyiw13JAm67UhRYyB1pM2mFQejabiRZZHERRIgnhMp8EhauOw1pjpgfIV66fHZfPUk0viK9U9FrtLRFqjZvinO-_-vPBnDs1X4JxGr7dpqB9-RkhmktT_leN8iLwRfSyP9-dAswbxxsUh6-iEWYks0lyBhnmxhVFi_BXG1EWBsvw_Wx6TVEG7o9F9EdgoiqsOsQnXYvX0n7UcdbSNQbDPqk4jc0GTbx6_WOrGsJJ6221HkL8QrcTmSXq5BqtppyDUjJRtQdIVT00fajOxUUQpQMRayPjoBf8rNQSCTAE4aJXTUEefZGHNL6wjy8ME9fmMeysDf6pj3kIfl1di4RLM_opNhThUAuAlSOw_uJnIyHf15t_W_Tt2GmclO79C7Pr6obMMu02KmkvBykup2e3EQvrhtsmUdE4GHSwvcB54FHog |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT8MwDLbGkBAceCMeA3KAE4SxNH3swGFiG4MB4gASnEqbphMCxrR2Avar-Cv8I5wsHQIBEgcOnJtGbezY_mT7M8CG5aBZlI6i2UesykPHpl4gJeUOjxEdeMJlqsH55NRpXPCjS_syBy9ZL4yuds9SkoOeBsXS1E6LnSguDhvfuGJdpwr67CoPTZkpq2zK50cEbcneYRUlvMlYvXa-36BmrgAVqHApDVRC04qCMhPMkcwOLc_hrmQht10pSizijrSZtKIwcm03liy2uAhjxBZCVUEJC_cdgVG-67leHkYrB1fNWmb9FQGeymSj1_WoOgjTqPP1V390hu8R7qekrPZ19Sl4zU5pUOJyu9NLwx3R_0Qg-Z-OcRomTeBNKoObMgM52Z6FKROEE2PiklmYOBkS2SZzcFY1M4jovR7bRfTkIKI677pEl-PLJ9K50XkYEvf6_WfSCO41STYJWq2ubGnNJw8dqesZknm4-JO_XIB8-6EtF4GUbUTjMULIAGMCDLPCUoRaogj3MUAIysESlDJt8IVhaFeDQu78Ibe0FpiPAvO1wHy2BFvDdzoDfpIfVxcyJfONrUp81SDkInDl-Hg705n3x9_vtvy75eswdlat-8eHp80VGGda61StXgHyabcnVzG4S8M1c58IXP-17r0BspRQhg |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Decision-making+model+under+complex+picture+fuzzy+Hamacher+aggregation+operators&rft.jtitle=Computational+%26+applied+mathematics&rft.au=Akram+Muhammad&rft.au=Bashir+Ayesha&rft.au=Garg+Harish&rft.date=2020-09-01&rft.pub=Springer+Nature+B.V&rft.issn=2238-3603&rft.eissn=1807-0302&rft.volume=39&rft.issue=3&rft_id=info:doi/10.1007%2Fs40314-020-01251-2&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2238-3603&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2238-3603&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2238-3603&client=summon |