{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T11:31:08Z","timestamp":1776425468453,"version":"3.51.2"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T00:00:00Z","timestamp":1761696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T00:00:00Z","timestamp":1761696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s40747-025-02078-2","type":"journal-article","created":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T06:14:50Z","timestamp":1761718490000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dombi aggregation operator in terms of complex bipolar fuzzy sets with application in decision making problems"],"prefix":"10.1007","volume":"11","author":[{"given":"Naveed","family":"Yaqoob","sequence":"first","affiliation":[]},{"given":"Muhammad","family":"Gulistan","sequence":"additional","affiliation":[]},{"given":"Muhammad Mohsin","family":"Abbas","sequence":"additional","affiliation":[]},{"given":"Khizar","family":"Hayat","sequence":"additional","affiliation":[]},{"given":"Mohammed M.","family":"Al-Shamiri","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,29]]},"reference":[{"issue":"3","key":"2078_CR1","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338\u2013353","journal-title":"Inf Control"},{"issue":"1","key":"2078_CR2","doi-asserted-by":"publisher","first-page":"87","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(1):87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"5","key":"2078_CR3","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1002\/int.21584","volume":"28","author":"RR Yager","year":"2013","unstructured":"Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28(5):436\u2013452","journal-title":"Int J Intell Syst"},{"key":"2078_CR4","unstructured":"Zhang WR (1994) Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In: NAFIPS\/IFIS\/NASA\u201994. Proceedings of the first international joint conference of the North American fuzzy information processing society biannual conference. The industrial fuzzy control and intelligent. IEEE, pp 305\u2013309"},{"key":"2078_CR5","doi-asserted-by":"crossref","unstructured":"Zhang WR (1998) (Yin)(Yang) bipolar fuzzy sets. In: 1998 IEEE international conference on fuzzy systems proceedings. IEEE world congress on computational intelligence (Cat. No. 98CH36228), vol 1. IEEE, pp 835\u2013840","DOI":"10.1109\/FUZZY.1998.687599"},{"issue":"2","key":"2078_CR6","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1109\/91.995119","volume":"10","author":"D Ramot","year":"2002","unstructured":"Ramot D, Milo R, Friedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171\u2013186","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"2078_CR7","first-page":"3981","volume":"40","author":"M Gulistan","year":"2021","unstructured":"Gulistan M, Yaqoob N, Elmoasry A, Alebraheem J (2021) Complex bipolar fuzzy sets: an application in a transport\u2019s company. J Intell Fuzzy Syst 40:3981\u20133997","journal-title":"J Intell Fuzzy Syst"},{"issue":"2","key":"2078_CR8","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/0165-0114(82)90005-7","volume":"8","author":"J Dombi","year":"1982","unstructured":"Dombi J (1982) A general class of fuzzy operators, the De-Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst 8(2):149\u2013163","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"2078_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1057\/s41274-017-0190-y","volume":"69","author":"P Liu","year":"2018","unstructured":"Liu P, Liu J, Chen SM (2018) Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J Oper Res Soc 69(1):1\u201324","journal-title":"J Oper Res Soc"},{"issue":"11","key":"2078_CR10","doi-asserted-by":"publisher","first-page":"3000","DOI":"10.1002\/int.22183","volume":"34","author":"M Akram","year":"2019","unstructured":"Akram M, Dudek WA, Dar JM (2019) Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision-making. Int J Intell Syst 34(11):3000\u20133019","journal-title":"Int J Intell Syst"},{"issue":"2","key":"2078_CR11","doi-asserted-by":"publisher","DOI":"10.1111\/exsy.12626","volume":"38","author":"M Akram","year":"2020","unstructured":"Akram M, Khan A, Borumand SA (2020) Complex Pythagorean Dombi fuzzy operators using aggregation operators and their decision-making. Expert Syst 38(2):e12626","journal-title":"Expert Syst"},{"issue":"2","key":"2078_CR12","first-page":"1977","volume":"38","author":"MR Hashmi","year":"2020","unstructured":"Hashmi MR, Riaz M (2020) A novel approach to censuses process by using Pythagorean m-polar fuzzy Dombi\u2019s aggregation operators. J Intell Fuzzy Syst 38(2):1977\u20131995","journal-title":"J Intell Fuzzy Syst"},{"issue":"4","key":"2078_CR13","doi-asserted-by":"publisher","first-page":"646","DOI":"10.3390\/sym13040646","volume":"13","author":"M Riaz","year":"2021","unstructured":"Riaz M, Khokhar MA, Pamucar D, Aslam M (2021) Cubic M-polar fuzzy hybrid aggregation operators with Dombi\u2019s T-norm and T-conorm with application. Symmetry 13(4):646","journal-title":"Symmetry"},{"issue":"2","key":"2078_CR14","first-page":"3373","volume":"41","author":"M Riaz","year":"2021","unstructured":"Riaz M, Habib A, Aslam M (2021) Cubic bipolar fuzzy Dombi averaging aggregation operators with application to multi-criteria decision-making. J Intell Fuzzy Syst 41(2):3373\u20133393","journal-title":"J Intell Fuzzy Syst"},{"key":"2078_CR15","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.cie.2017.12.024","volume":"116","author":"Q Wu","year":"2018","unstructured":"Wu Q, Wu P, Zhou L, Chen H, Guan X (2018) Some new Hamacher aggregation operators under single-valued neutrosophic 2-tuple linguistic environment and their applications to multi-attribute group decision making. Comput Ind Eng 116:144\u2013162","journal-title":"Comput Ind Eng"},{"key":"2078_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106757","volume":"98","author":"Q Wu","year":"2021","unstructured":"Wu Q, Liu X, Qin J, Wang W, Zhou L (2021) A linguistic distribution behavioral multi-criteria group decision making model integrating extended generalized TODIM and quantum decision theory. Appl Soft Comput 98:106757","journal-title":"Appl Soft Comput"},{"key":"2078_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.108794","volume":"249","author":"Q Wu","year":"2022","unstructured":"Wu Q, Liu X, Qin J, Zhou L, Mardani A, Deveci M (2022) An integrated generalized TODIM model for portfolio selection based on financial performance of firms. Knowl Based Syst 249:108794","journal-title":"Knowl Based Syst"},{"key":"2078_CR18","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1016\/j.ins.2021.04.096","volume":"570","author":"Q Wu","year":"2021","unstructured":"Wu Q, Liu X, Qin J, Zhou L (2021) Multi-criteria group decision-making for portfolio allocation with consensus reaching process under interval type-2 fuzzy environment. Inf Sci 570:668\u2013688","journal-title":"Inf Sci"},{"key":"2078_CR19","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1016\/j.ins.2019.06.049","volume":"502","author":"Q Wu","year":"2019","unstructured":"Wu Q, Zhou L, Chen Y, Chen H (2019) An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods. Inf Sci 502:394\u2013417","journal-title":"Inf Sci"},{"key":"2078_CR20","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.asoc.2018.10.021","volume":"74","author":"C Jana","year":"2019","unstructured":"Jana C, Senapati T, Pal M, Yager RR (2019) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74:99\u2013109","journal-title":"Appl Soft Comput"},{"issue":"11","key":"2078_CR21","doi-asserted-by":"publisher","first-page":"6645","DOI":"10.1002\/int.22563","volume":"36","author":"A Saha","year":"2021","unstructured":"Saha A, Senapati T, Yager RR (2021) Hybridizations of generalized Dombi operators and Bonferroni mean operators under dual probabilistic linguistic environment for group decision-making. Int J Intell Syst 36(11):6645\u20136679","journal-title":"Int J Intell Syst"},{"issue":"9","key":"2078_CR22","doi-asserted-by":"publisher","first-page":"2019","DOI":"10.1002\/int.22125","volume":"34","author":"C Jana","year":"2019","unstructured":"Jana C, Senapati T, Pal M (2019) Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int J Intell Syst 34(9):2019\u20132038","journal-title":"Int J Intell Syst"},{"issue":"9","key":"2078_CR23","doi-asserted-by":"publisher","first-page":"3533","DOI":"10.1007\/s12652-018-1076-9","volume":"10","author":"C Jana","year":"2019","unstructured":"Jana C, Pal M, Wang JQ (2019) Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process. J Ambient Intell Humaniz Comput 10(9):3533\u20133549","journal-title":"J Ambient Intell Humaniz Comput"},{"issue":"1","key":"2078_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40815-017-0338-6","volume":"20","author":"G Wei","year":"2018","unstructured":"Wei G, Alsaadi FE, Hayat T, Alsaedi A (2018) Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. Int J Fuzzy Syst 20(1):1\u201312","journal-title":"Int J Fuzzy Syst"},{"issue":"21","key":"2078_CR25","doi-asserted-by":"publisher","first-page":"13353","DOI":"10.1007\/s00500-021-06181-7","volume":"25","author":"K Hayat","year":"2021","unstructured":"Hayat K, Tariq Z, Lughofer E, Aslam MF (2021) New aggregation operators on group-based generalized intuitionistic fuzzy soft sets. Soft Comput 25(21):13353\u201313364","journal-title":"Soft Comput"},{"issue":"11","key":"2078_CR26","first-page":"1","volume":"15","author":"M Waqar","year":"2022","unstructured":"Waqar M, Ullah K, Pamucar D, Jovanov G, Vranje D (2022) An approach for the analysis of energy resource selection based on attributes by using Dombi T-norm based aggregation operators. Energies MDPI 15(11):1\u201323","journal-title":"Energies MDPI"},{"issue":"17","key":"2078_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.heliyon.2024.e36461","volume":"10","author":"Z Zhao","year":"2024","unstructured":"Zhao Z, Hussain A, Zhang N, Ullah K, Yin S, Awsar A, El-Bahy SM (2024) Decision support system based on bipolar complex fuzzy Hamy mean operators. Heliyon 10(17):e36461","journal-title":"Heliyon"},{"issue":"1","key":"2078_CR28","doi-asserted-by":"publisher","first-page":"1848","DOI":"10.3934\/math.2023095","volume":"8","author":"T Mahmood","year":"2023","unstructured":"Mahmood T, Rehman UU, Naeem M (2023) A novel approach towards Heronian mean operators in multiple attribute decision making under the environment of bipolar complex fuzzy information. AIMS Math 8(1):1848\u20131870. https:\/\/doi.org\/10.3934\/math.2023095","journal-title":"AIMS Math"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02078-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-02078-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02078-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T08:39:59Z","timestamp":1763627999000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-02078-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,29]]},"references-count":28,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["2078"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-02078-2","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,29]]},"assertion":[{"value":"9 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 November 2025","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The original publication was revised due to update in acknowledgment text.","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors of this paper declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical statement"}}],"article-number":"483"}}