{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T04:01:40Z","timestamp":1788494500356,"version":"build-2803163510"},"reference-count":71,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T00:00:00Z","timestamp":1715817600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T00:00:00Z","timestamp":1715817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Artif Intell Rev"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In some multi-criteria decision-making (MCDM) scenarios, decision makers must address challenges like handling uncertain and incomplete information, managing biases in criteria values, and assessing interrelationships among criteria based on their partitioning as per their characteristics. To tackle these challenges, a picture fuzzy set (PFS) can be utilized to quantify vague information, Hamy mean (HM) can be used to consider criteria interrelationships while the power average (PA) mitigates any kind of biasness. Also, to overcome the limitations of persistence and invariantess in algebraic operations, Dempster-Shafer theory (DST) is employed. By integrating the conventional HM with the traditional PA under partitioning, this paper first introduced the novel power partitioned Hamy mean (<jats:inline-formula><jats:alternatives><jats:tex-math>$$PPtHM^q$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>P<\/mml:mi><mml:mi>P<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>H<\/mml:mi><mml:msup><mml:mi>M<\/mml:mi><mml:mi>q<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) operator. Then, this operator is extended for picture fuzzy numbers (PFNs) with DST and two novel operators are introduced, which are named as picture fuzzy power partitioned Hamy mean<jats:inline-formula><jats:alternatives><jats:tex-math>$$(PFPPtHM^q_{DST})$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>P<\/mml:mi><mml:mi>F<\/mml:mi><mml:mi>P<\/mml:mi><mml:mi>P<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>H<\/mml:mi><mml:msubsup><mml:mi>M<\/mml:mi><mml:mrow><mml:mi>DST<\/mml:mi><\/mml:mrow><mml:mi>q<\/mml:mi><\/mml:msubsup><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and picture fuzzy weighted power partitioned Hamy mean<jats:inline-formula><jats:alternatives><jats:tex-math>$$(PFWPPtHM^q_{DST})$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>P<\/mml:mi><mml:mi>F<\/mml:mi><mml:mi>W<\/mml:mi><mml:mi>P<\/mml:mi><mml:mi>P<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>H<\/mml:mi><mml:msubsup><mml:mi>M<\/mml:mi><mml:mrow><mml:mi>DST<\/mml:mi><\/mml:mrow><mml:mi>q<\/mml:mi><\/mml:msubsup><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>with some desirable properties. Moreover, based on these operators, a new method for MCDM in the PFS environment has been designed. The paper illustrates their application in selecting the best hotel among four alternatives (<jats:inline-formula><jats:alternatives><jats:tex-math>$$B_1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$B_2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$B_3$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mn>3<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$B_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mn>4<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) based on five criteria, which are partitioned into two sets. Results indicate that the best and worst alternatives under these operators are hotels<jats:inline-formula><jats:alternatives><jats:tex-math>$$B_1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$B_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mn>4<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, respectively. Sensitivity analysis explores the impact of granularity parameter variations, and comparative analysis demonstrates the effectiveness of the presented operators. Overall, the study concludes that these operators offer flexibility, generality, and consistency for analyzing MCDM problems in PFS environments.<\/jats:p>","DOI":"10.1007\/s10462-024-10757-8","type":"journal-article","created":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T12:01:56Z","timestamp":1715860916000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Novel picture fuzzy power partitioned Hamy mean operators with Dempster-Shafer theory and their applications in MCDM"],"prefix":"10.1007","volume":"57","author":[{"given":"Tanuja","family":"Punetha","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"family":"Komal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dragan","family":"Pamucar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,16]]},"reference":[{"key":"10757_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-023-08154-4","author":"U Ahmad","year":"2023","unstructured":"Ahmad U, Khan A, Saeid AB (2023) Integrated multi-criteria group decision-making methods based on q-rung picture fuzzy sets for the identification of occupational hazards. Soft Comput. https:\/\/doi.org\/10.1007\/s00500-023-08154-4","journal-title":"Soft Comput"},{"key":"10757_CR2","doi-asserted-by":"crossref","first-page":"5541","DOI":"10.1007\/s10462-021-10027-x","volume":"54","author":"M Akram","year":"2021","unstructured":"Akram M, Ali G, Alcantud JCR (2021) Parameter reduction analysis under interval-valued m-polar fuzzy soft information. Artif Intell Rev 54:5541\u20135582","journal-title":"Artif Intell Rev"},{"key":"10757_CR3","first-page":"9915432","volume":"2021","author":"M Akram","year":"2021","unstructured":"Akram M, Alsulami S, Zahid K (2021) A hybrid method for complex pythagorean fuzzy decision-making. Math Probl Eng 2021:9915432","journal-title":"Math Probl Eng"},{"key":"10757_CR4","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1007\/s00521-020-05034-y","volume":"33","author":"M Akram","year":"2021","unstructured":"Akram M, Habib A, Alcantud JCR (2021) An optimization study based on Dijkstra algorithm for a network with trapezoidal picture fuzzy numbers. Neural Computing & Applications 33:1329\u20131342","journal-title":"Neural Computing & Applications"},{"key":"10757_CR5","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2023.110403","volume":"143","author":"M Akram","year":"2023","unstructured":"Akram M, Zahid K, Deveci M (2023) Multi-criteria group decision-making for optimal management of water supply with fuzzy ELECTRE-based outranking method. Appl Soft Comput 143:110403","journal-title":"Appl Soft Comput"},{"key":"10757_CR6","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2023.109992","volume":"134","author":"M Akram","year":"2023","unstructured":"Akram M, Zahid K, Kahraman C (2023) Integrated outranking techniques based on spherical fuzzy information for the digitalization of transportation system. Appl Soft Comput 134:109992","journal-title":"Appl Soft Comput"},{"key":"10757_CR7","doi-asserted-by":"crossref","first-page":"10227","DOI":"10.1007\/s10462-023-10408-4","volume":"56","author":"M Akram","year":"2023","unstructured":"Akram M, Naz S, Abbas T (2023) Complex q-rung orthopair fuzzy 2-tuple linguistic group decision-making framework with Muirhead mean operators. Artif Intell Rev 56:10227\u201310274","journal-title":"Artif Intell Rev"},{"issue":"7","key":"10757_CR8","volume":"97","author":"J Ali","year":"2022","unstructured":"Ali J (2022) Hesitant fuzzy partitioned Maclaurin symmetric mean aggregation operators in multi-criteria decision-making. Phys Scr 97(7):075208","journal-title":"Phys Scr"},{"issue":"4","key":"10757_CR9","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1007\/s40314-023-02313-x","volume":"42","author":"J Ali","year":"2023","unstructured":"Ali J (2023) Norm-based distance measure of q-rung orthopair fuzzy sets and its application in decision-making. Comput Appl Math 42(4):184","journal-title":"Comput Appl Math"},{"issue":"6","key":"10757_CR10","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1007\/s40314-023-02387-7","volume":"42","author":"J Ali","year":"2023","unstructured":"Ali J (2023) Probabilistic hesitant bipolar fuzzy Hamacher prioritized aggregation operators and their application in multi-criteria group decision-making. Comput Appl Math 42(6):260","journal-title":"Comput Appl Math"},{"key":"10757_CR11","volume":"119","author":"J Ali","year":"2023","unstructured":"Ali J, Garg H (2023) On spherical fuzzy distance measure and TAOV method for decision-making problems with incomplete weight information. Eng Appl Artif Intell 119:105726","journal-title":"Eng Appl Artif Intell"},{"key":"10757_CR12","doi-asserted-by":"crossref","first-page":"46454","DOI":"10.1109\/ACCESS.2023.3271141","volume":"11","author":"J Ali","year":"2023","unstructured":"Ali J, Naeem M (2023) r, s, t-spherical fuzzy VIKOR method and its application in multiple criteria group decision making. IEEE Access 11:46454\u201346475","journal-title":"IEEE Access"},{"key":"10757_CR13","doi-asserted-by":"crossref","first-page":"49081","DOI":"10.1109\/ACCESS.2023.3274494","volume":"11","author":"J Ali","year":"2023","unstructured":"Ali J, Naeem M (2023) Analysis and application of p, q-quasirung orthopair fuzzy Aczel-Alsina aggregation operators in multiple criteria decision-making. IEEE Access 11:49081\u201349101","journal-title":"IEEE Access"},{"key":"10757_CR14","doi-asserted-by":"crossref","first-page":"88971","DOI":"10.1109\/ACCESS.2023.3298845","volume":"11","author":"J Ali","year":"2023","unstructured":"Ali J, Naeem M, Al-Kenani AN (2023) Complex T-spherical fuzzy Frank aggregation operators and their application to decision making. IEEE Access 11:88971\u201389023","journal-title":"IEEE Access"},{"key":"10757_CR15","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:89\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"10757_CR16","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1002\/int.22220","volume":"35","author":"F Ates","year":"2020","unstructured":"Ates F, Akay D (2020) Some picture fuzzy Bonferroni mean operators with their application to multi criteria decision making. Int J Intell Syst 35(4):625\u2013649","journal-title":"Int J Intell Syst"},{"key":"10757_CR17","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1186\/s40854-022-00443-5","volume":"9","author":"S Biswas","year":"2023","unstructured":"Biswas S, Pamucar D (2023) A modified EDAS model for comparison of mobile wallet service providers in India. Financial Innovation 9:41","journal-title":"Financial Innovation"},{"key":"10757_CR18","first-page":"267","volume":"5","author":"C Bonferroni","year":"1950","unstructured":"Bonferroni C (1950) Sulle media multiple di potenze. Bollettino dell\u2019Unione Matematica Italiana 5:267\u2013270","journal-title":"Bollettino dell\u2019Unione Matematica Italiana"},{"key":"10757_CR19","first-page":"409","volume":"30","author":"BC Cuong","year":"2014","unstructured":"Cuong BC (2014) Picture fuzzy sets. Journal of Computer Science and Cybernetics 30:409\u2013420","journal-title":"Journal of Computer Science and Cybernetics"},{"issue":"1","key":"10757_CR20","doi-asserted-by":"crossref","first-page":"39","DOI":"10.31181\/jscda1120233","volume":"1","author":"HA Dagistanli","year":"2023","unstructured":"Dagistanli HA (2023) An integrated fuzzy MCDM and trend analysis approach for financial performance evaluation of energy companies in Borsa Istanbul sustainability index. Journal of Soft Computing and Decision Analytics 1(1):39\u201349","journal-title":"Journal of Soft Computing and Decision Analytics"},{"issue":"1","key":"10757_CR21","doi-asserted-by":"crossref","first-page":"50","DOI":"10.31181\/jscda1120234","volume":"1","author":"H Dincer","year":"2023","unstructured":"Dincer H, Y\u00fcksel S, Eti S (2023) Identifying the right policies for increasing the efficiency of the renewable energy transition with a novel fuzzy decision-making model. Journal of Soft Computing and Decision Analytics 1(1):50\u201362","journal-title":"Journal of Soft Computing and Decision Analytics"},{"key":"10757_CR22","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","volume":"38","author":"AP Dempster","year":"1967","unstructured":"Dempster AP (1967) Upper and lower probabilities induced by multi valued mapping. Annals of the Mathematical Statistics 38:325\u2013339","journal-title":"Annals of the Mathematical Statistics"},{"key":"10757_CR23","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.asoc.2015.08.017","volume":"37","author":"B Dutta","year":"2015","unstructured":"Dutta B, Guha D (2015) Partitioned Bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making. Appl Soft Comput 37:166\u2013179","journal-title":"Appl Soft Comput"},{"issue":"4","key":"10757_CR24","first-page":"15","volume":"7","author":"P Dutta","year":"2018","unstructured":"Dutta P (2018) Medical diagnosis based on distance measures between picture fuzzy sets. Int J Fuzzy Syst 7(4):15\u201336","journal-title":"Int J Fuzzy Syst"},{"key":"10757_CR25","doi-asserted-by":"crossref","first-page":"12609","DOI":"10.1007\/s00521-020-04715-y","volume":"32","author":"AH Ganie","year":"2020","unstructured":"Ganie AH, Singh S, Bhatia PK (2020) Some new correlation coefficients of picture fuzzy sets with applications. Neural Comput Appl 32:12609\u201312625","journal-title":"Neural Comput Appl"},{"key":"10757_CR26","doi-asserted-by":"crossref","first-page":"9199","DOI":"10.1007\/s00521-020-05682-0","volume":"33","author":"AH Ganie","year":"2021","unstructured":"Ganie AH, Singh S (2021) A picture fuzzy similarity measure based on direct operations and novel multi-attribute decision-making. Neural Comput Appl 33:9199\u20139219","journal-title":"Neural Comput Appl"},{"issue":"12","key":"10757_CR27","doi-asserted-by":"crossref","first-page":"5275","DOI":"10.1007\/s13369-017-2625-9","volume":"42","author":"H Garg","year":"2017","unstructured":"Garg H (2017) Some picture fuzzy aggregation operators and their application to multi criteria decision making. Arab J Sci Eng 42(12):5275\u20135290","journal-title":"Arab J Sci Eng"},{"issue":"4","key":"10757_CR28","first-page":"387","volume":"2","author":"T Hara","year":"1998","unstructured":"Hara T, Uchiyama M, Takahasi SE (1998) A refinement of various mean inequalities. Journal of Inequalities and Applications 2(4):387\u2013395","journal-title":"Journal of Inequalities and Applications"},{"issue":"2","key":"10757_CR29","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1142\/s0218488515500129","volume":"23","author":"Y He","year":"2015","unstructured":"He Y, He Z, Jin C, Chen H (2015) Intuitionistic fuzzy power geometric Bonferroni means and their application to multiple attribute decision making. International Journal of Uncertainty, Fuzziness And Knowledge based Systems 23(2):285\u2013315","journal-title":"International Journal of Uncertainty, Fuzziness And Knowledge based Systems"},{"key":"10757_CR30","doi-asserted-by":"crossref","unstructured":"Jana C, Senapati T, Pal M, Yager RR (2018) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74:99\u2013109","DOI":"10.1016\/j.asoc.2018.10.021"},{"issue":"4","key":"10757_CR31","doi-asserted-by":"crossref","first-page":"556","DOI":"10.5391\/JKIIS.2009.19.4.556","volume":"19","author":"HP Jin","year":"2009","unstructured":"Jin HP, Ki ML, Young CK (2009) Distance measure between intuitionistic fuzzy set and its application to pattern recognition. Journal of Korean Institute of Intelligent Systems 19(4):556\u2013561","journal-title":"Journal of Korean Institute of Intelligent Systems"},{"issue":"1","key":"10757_CR32","doi-asserted-by":"crossref","first-page":"51236","DOI":"10.1109\/ACCESS.2019.2910844","volume":"7","author":"AM Khalil","year":"2019","unstructured":"Khalil AM, Li SG, Garg H, Li H, Ma S (2019) New operators on interval valued picture fuzzy set, Interval-valued picture fuzzy soft sets and their applications. IEEE Access 7(1):51236\u201351253","journal-title":"IEEE Access"},{"key":"10757_CR33","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s40096-019-0291-7","volume":"13","author":"S Khan","year":"2019","unstructured":"Khan S, Abdullah S, Ashraf S (2019) Picture fuzzy aggregation information based on Einstein operations and their applications in decision making. Mathematical Sciences 13:213\u2013229","journal-title":"Mathematical Sciences"},{"key":"10757_CR34","volume":"53","author":"M Lin","year":"2020","unstructured":"Lin M, Huang C, Xu Z (2020) MULTIMOORA based MCDM model for site selection of car sharing station under picture fuzzy environment. Sustain Cities Soc 53:101873","journal-title":"Sustain Cities Soc"},{"key":"10757_CR35","first-page":"1","volume":"4","author":"D Liu","year":"2017","unstructured":"Liu D (2017) Interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure and its applications in investment decision making. Complexity 4:1\u201311","journal-title":"Complexity"},{"issue":"3","key":"10757_CR36","doi-asserted-by":"crossref","first-page":"1755","DOI":"10.1002\/int.22114","volume":"34","author":"P Liu","year":"2019","unstructured":"Liu P, Liu W (2019) Multi attribute group decision making method of linguistic q-rung orthopair fuzzy power Muirhead mean operators based on entropy weight. Int J Intell Syst 34(3):1755\u20131794","journal-title":"Int J Intell Syst"},{"issue":"2","key":"10757_CR37","doi-asserted-by":"crossref","first-page":"293","DOI":"10.15388\/Informatica.2019.207","volume":"30","author":"P Liu","year":"2019","unstructured":"Liu P, Khan Q, Mahmood T (2019) Application of interval neutrosophic power Hamy mean operators in MAGDM. Informatica 30(2):293\u2013325","journal-title":"Informatica"},{"issue":"1","key":"10757_CR38","volume":"85","author":"P Liu","year":"2020","unstructured":"Liu P, Gao H (2020) Some intuitionistic fuzzy power Bonferroni mean operators in the framework of Dempster-Shafer theory and their application to multi criteria decision making. Appl Soft Comput 85(1):105790","journal-title":"Appl Soft Comput"},{"key":"10757_CR39","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1007\/s40815-019-00736-5","volume":"22","author":"Z Liu","year":"2020","unstructured":"Liu Z, Xu H, Liu P, Li L, Zhao X (2020) Interval-valued intuitionistic uncertain linguistic multi attribute decision-making method for plant location selection with partitioned Hamy mean. Int J Fuzzy Syst 22:1993\u20132010","journal-title":"Int J Fuzzy Syst"},{"issue":"1","key":"10757_CR40","doi-asserted-by":"crossref","first-page":"3","DOI":"10.3390\/math8010003","volume":"8","author":"S Luo","year":"2020","unstructured":"Luo S, Xing L (2020) Picture fuzzy interaction partitioned Heronian aggregation operators for Hotel selection. Mathematics 8(1):3","journal-title":"Mathematics"},{"key":"10757_CR41","unstructured":"Maclaurin C (1729) A second letter to Martin folkes Esq .;concerning the roots of equations, with demonstration of other rules of algebra. Philosophical Transactions of the Royal Society B: Biological Sciences 3(6):59\u201396"},{"key":"10757_CR42","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1017\/S001309150003460X","volume":"21","author":"RF Muirhead","year":"1902","unstructured":"Muirhead RF (1902) Some methods applicable to identities and inequalities of symmetric algebraic function of n letters. Proc Edinb Math Soc 21:144\u2013162","journal-title":"Proc Edinb Math Soc"},{"key":"10757_CR43","doi-asserted-by":"crossref","unstructured":"Naseem A, Akram M, Ullah K, Ali Z (2023) Aczel-Alsina Aggregation operators based on complex single-valued neutrosophic information and their application in decision-making problems. Decision Making Advances 1(1):86\u2013114","DOI":"10.31181\/dma11202312"},{"key":"10757_CR44","doi-asserted-by":"crossref","unstructured":"Punetha T, Komal (2023) Picture fuzzy power Muirhead mean operators and their application to multi attribute decision making. J Ind Manag Opt 19(6):4321\u20134349","DOI":"10.3934\/jimo.2022132"},{"issue":"11","key":"10757_CR45","volume":"149","author":"Y Qin","year":"2020","unstructured":"Qin Y, Qi Q, Shi P, Scott PJ, Jiang X (2020) Novel operational laws and power Muirhead mean operators of picture fuzzy values in the framework of Dempster-Shafer theory for multiple criteria decision making. Computers & Industrial Engineering 149(11):106853","journal-title":"Computers & Industrial Engineering"},{"key":"10757_CR46","doi-asserted-by":"crossref","first-page":"12329","DOI":"10.1007\/s00500-020-04676-3","volume":"24","author":"Y Qin","year":"2020","unstructured":"Qin Y, Qi Q, Scott PJ, Jiang X (2020) Multiple criteria decision making based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalized orthopair membership grades. Soft Comput 24:12329\u201312355","journal-title":"Soft Comput"},{"key":"10757_CR47","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1007\/s41066-020-00228-0","volume":"6","author":"Q Qin","year":"2021","unstructured":"Qin Q, Cui X, Huang M, Zhong Y, Tang Z, Shi P (2021) Multi attribute decision making based on picture fuzzy archimedean power Maclaurin symmetric mean. Granular Computing 6:737\u2013761","journal-title":"Granular Computing"},{"issue":"2","key":"10757_CR48","first-page":"639","volume":"6","author":"MJ Ranjan","year":"2023","unstructured":"Ranjan MJ, Kumar BP, Bhavani TD, Padmavathi AV, Bakka V (2023) Probabilistic linguistic q-rung orthopair fuzzy Archimedean aggregation operators for group decision-making. Decision Making: Applications in Management and Engineering 6(2):639\u2013667","journal-title":"Decision Making: Applications in Management and Engineering"},{"key":"10757_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-023-01201-5","author":"SS Rawat","year":"2023","unstructured":"Rawat SS, Komal Liu P, Stevic P, Senapati T, Moslem S (2023) A novel group decision-making approach based on partitioning Hamy mean operators in q-rung orthopair fuzzy context. Complex & Intelligent Systems. https:\/\/doi.org\/10.1007\/s40747-023-01201-5","journal-title":"Complex & Intelligent Systems"},{"issue":"1","key":"10757_CR50","doi-asserted-by":"crossref","first-page":"25","DOI":"10.31181\/dma1120237","volume":"1","author":"SK Sahoo","year":"2023","unstructured":"Sahoo SK, Goswami SS (2023) A comprehensive review of multiple criteria decision-making (MCDM) methods: advancements, applications, and future directions. Decision Making Advances 1(1):25\u201348","journal-title":"Decision Making Advances"},{"key":"10757_CR51","doi-asserted-by":"crossref","first-page":"447","DOI":"10.31449\/inf.v45i3.3025","volume":"45","author":"MR Seikh","year":"2021","unstructured":"Seikh MR, Mandal U (2021) Some picture fuzzy aggregation operators based on Frank $$t$$-norm and $$t$$-conorm: Application to MADM process. Informatica 45:447\u2013461","journal-title":"Informatica"},{"key":"10757_CR52","doi-asserted-by":"crossref","DOI":"10.1515\/9780691214696","volume-title":"A mathematical theory of evidence","author":"G Shafer","year":"1976","unstructured":"Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton"},{"key":"10757_CR53","doi-asserted-by":"crossref","first-page":"3327","DOI":"10.1007\/s00500-021-05909-9","volume":"27","author":"A Si","year":"2021","unstructured":"Si A, Das S, Kar S (2021) Picture fuzzy set-based decision-making approach using Dempster-Shafer theory of evidence and grey relation analysis and its application in COVID-19 medicine selection. Soft Comput 27:3327\u20133341","journal-title":"Soft Comput"},{"key":"10757_CR54","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s41066-020-00218-2","volume":"6","author":"A Singh","year":"2020","unstructured":"Singh A, Kumar S (2020) Picture fuzzy choquet integral based VIKOR for multi criteria group decision making problems. Granular Computing 6:587\u2013601","journal-title":"Granular Computing"},{"issue":"5","key":"10757_CR55","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TFUZZ.2012.2189405","volume":"20","author":"W Wang","year":"2012","unstructured":"Wang W, Liu X (2012) Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20(5):923\u2013938","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"10757_CR56","doi-asserted-by":"crossref","first-page":"6","DOI":"10.3390\/sym11010006","volume":"11","author":"R Wang","year":"2018","unstructured":"Wang R, Wang J, Gao H, Wei G (2018) Methods for MADM with picture fuzzy Muirhead Mean operators and their application for evaluating the financial investment risk. Symmetry 11(1):6","journal-title":"Symmetry"},{"key":"10757_CR57","first-page":"477","volume":"37","author":"C Wang","year":"2017","unstructured":"Wang C, Zhou X, Tu H, Tao S (2017) Some geometric aggregation operators based on picture fuzzy sets and their applications in multiple attribute decision making. Italian Journal of Pure and Applied Mathematics 37:477\u2013492","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"issue":"3","key":"10757_CR58","doi-asserted-by":"crossref","first-page":"547","DOI":"10.15388\/Informatica.2017.144","volume":"28","author":"G Wei","year":"2017","unstructured":"Wei G (2017) Some cosine similarity measure for picture fuzzy sets and their applications to strategic decision making. Informatica 28(3):547\u2013564","journal-title":"Informatica"},{"key":"10757_CR59","doi-asserted-by":"crossref","first-page":"713","DOI":"10.3233\/JIFS-161798","volume":"33","author":"G Wei","year":"2017","unstructured":"Wei G (2017) Picture fuzzy aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems 33:713\u2013724","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"10757_CR60","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3233\/FI-2018-1628","volume":"157","author":"G Wei","year":"2018","unstructured":"Wei G (2018) Picture fuzzy Hamacher Aggregation operators and their applications to multi attribute decision making. Fandamenta Informaticae 157:271\u2013320","journal-title":"Fandamenta Informaticae"},{"key":"10757_CR61","doi-asserted-by":"crossref","first-page":"167","DOI":"10.3233\/KES-180382","volume":"22","author":"G Wei","year":"2018","unstructured":"Wei G, Lu M, Gao H (2018) Picture fuzzy Heronian mean aggregation operators in multiple attribute decision making. International Journal of Knowledge-Based Intelligent Engineering Systems 22:167\u2013175","journal-title":"International Journal of Knowledge-Based Intelligent Engineering Systems"},{"issue":"6","key":"10757_CR62","first-page":"1176","volume":"14","author":"Z Xu","year":"2008","unstructured":"Xu Z (2008) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 14(6):1176\u20131189","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"10757_CR63","first-page":"94","volume":"18","author":"Z Xu","year":"2009","unstructured":"Xu Z, Yager RR (2009) Power-geometric operators and their use in group decision making. IEEE Trans Fuzzy Syst 18:94\u2013105","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"6","key":"10757_CR64","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/3468.983429","volume":"31","author":"RR Yager","year":"2001","unstructured":"Yager RR (2001) The power average operator. IEEE System, Man and Cybernetics Society 31(6):724\u2013731","journal-title":"IEEE System, Man and Cybernetics Society"},{"key":"10757_CR65","first-page":"1079","volume":"24","author":"Z Yang","year":"2021","unstructured":"Yang Z, Garg H (2021) Interaction power partitioned Maclaurin symmetric mean operators under q-rung orthopair uncertain linguistic information. Int J Fuzzy Syst 24:1079\u20131097","journal-title":"Int J Fuzzy Syst"},{"issue":"3","key":"10757_CR66","volume":"9","author":"X Yang","year":"2023","unstructured":"Yang X, Mahmood T, Ahmmad J (2023) Picture fuzzy soft Bonferroni mean aggregation operators and their applications. Heliyon 9(3):e17278","journal-title":"Heliyon"},{"issue":"1","key":"10757_CR67","first-page":"50","volume":"5","author":"BF Yildirim","year":"2022","unstructured":"Yildirim BF, Yildirim KS (2022) Evaluating the satisfaction level of citizens in municipality services by using picture fuzzy VIKOR method: 2014\u20132019 period analysis. Decision Making: Applications in Management and Engineering 5(1):50\u201366","journal-title":"Decision Making: Applications in Management and Engineering"},{"key":"10757_CR68","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s11192-015-1695-2","volume":"105","author":"D Yu","year":"2015","unstructured":"Yu D (2015) A scientometrics review on aggregation operator reserach. Scientometrics 105:115\u2013133","journal-title":"Scientometrics"},{"key":"10757_CR69","doi-asserted-by":"crossref","unstructured":"Zadeh LA (1965) Fuzzy Sets Inf Control 8(3):338\u2013356","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"10757_CR70","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.cie.2019.05.006","volume":"133","author":"H Zhang","year":"2019","unstructured":"Zhang H, Xie J, Lu W, Zhang Z, Fu X (2019) Novel ranking method for intuitionistic fuzzy values based on information fusion. Computers & Industrial Engineering 133:139\u2013152","journal-title":"Computers & Industrial Engineering"},{"key":"10757_CR71","doi-asserted-by":"crossref","unstructured":"Zhang L, Zhan J, Yao Y (2020) Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems. Inf Sci 517:315\u2013339","DOI":"10.1016\/j.ins.2020.01.003"}],"container-title":["Artificial Intelligence Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10462-024-10757-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10462-024-10757-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10462-024-10757-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T05:41:38Z","timestamp":1731994898000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10462-024-10757-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,16]]},"references-count":71,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["10757"],"URL":"https:\/\/doi.org\/10.1007\/s10462-024-10757-8","relation":{},"ISSN":["1573-7462"],"issn-type":[{"value":"1573-7462","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,16]]},"assertion":[{"value":"1 April 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants or animals preformed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The authors declare that they have no conflict of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"145"}}