{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T17:48:37Z","timestamp":1771350517748,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T00:00:00Z","timestamp":1708387200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T00:00:00Z","timestamp":1708387200000},"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":["Complex Intell. Syst."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In 1960, Schweizer and Sklar introduced the novel Schweizer-Sklar t-norm and t-conorm which is used in the construction of aggregation operators. Schweizer-Sklar norms are more general than algebraic norms and Einstein norms. Additionally, computing the power operators based on the Schweizer-Sklar norms for complex Atanassov intuitionistic fuzzy (CA-IF) set is very awkward and complicated. In this manuscript, firstly, we propose the Schweizer-Sklar operational laws for CA-IF values, and secondly, we develop the CA-IF Schweizer-Sklar power averaging (CA-IFSSPA) operator, CA-IF Schweizer-Sklar power ordered averaging (CA-IFSSPOA) operator, CA-IF Schweizer-Sklar power geometric (CA-IFSSPG) operator, and CA-IF Schweizer-Sklar power ordered geometric (CA-IFSSPOG) operator. Some suitable and dominant properties for the above operators are also discussed. Furthermore, to simplify the above operators, we develop the procedure of decision-making technique, called multi-attribute decision-making (MADM) methods based on the proposed operators based on CA-IF values. Finally, we compare the proposed methods with some existing methods to describe the efficiency and capability of the discovered approaches by some examples.<\/jats:p>","DOI":"10.1007\/s40747-023-01331-w","type":"journal-article","created":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T02:02:35Z","timestamp":1708394555000},"page":"3673-3690","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Schweizer-Sklar power aggregation operators based on complex intuitionistic fuzzy information and their application in decision-making"],"prefix":"10.1007","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5048-8145","authenticated-orcid":false,"given":"Peide","family":"Liu","sequence":"first","affiliation":[]},{"given":"Zeeshan","family":"Ali","sequence":"additional","affiliation":[]},{"given":"Tahir","family":"Mahmood","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,2,20]]},"reference":[{"issue":"3","key":"1331_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":"18","key":"1331_CR2","doi-asserted-by":"publisher","first-page":"9011","DOI":"10.1007\/s00500-022-07254-x","volume":"26","author":"T Mahmood","year":"2022","unstructured":"Mahmood T, Ali Z (2022) Fuzzy superior mandelbrot sets. Soft Comput 26(18):9011\u20139020","journal-title":"Soft Comput"},{"issue":"1","key":"1331_CR3","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"12","key":"1331_CR4","doi-asserted-by":"publisher","first-page":"715","DOI":"10.3390\/axioms11120715","volume":"11","author":"T Mahmood","year":"2022","unstructured":"Mahmood T, Ali Z, Baupradist S, Chinram R (2022) TOPSIS method based on hamacher choquet-integral aggregation operators for atanassov-intuitionistic fuzzy sets and their applications in decision-making. Axioms 11(12):715","journal-title":"Axioms"},{"key":"1331_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.116242","volume":"191","author":"X Jia","year":"2022","unstructured":"Jia X, Wang Y (2022) Choquet integral-based intuitionistic fuzzy arithmetic aggregation operators in multi-criteria decision-making. Expert Syst Appl 191:116242","journal-title":"Expert Syst Appl"},{"issue":"2","key":"1331_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"},{"issue":"3","key":"1331_CR7","doi-asserted-by":"publisher","first-page":"3351","DOI":"10.3233\/JIFS-191718","volume":"39","author":"P Liu","year":"2020","unstructured":"Liu P, Ali Z, Mahmood T (2020) The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making. J Intell Fuzzy Syst 39(3):3351\u20133374","journal-title":"J Intell Fuzzy Syst"},{"key":"1331_CR8","doi-asserted-by":"publisher","first-page":"73506","DOI":"10.1109\/ACCESS.2021.3074590","volume":"9","author":"T Mahmood","year":"2021","unstructured":"Mahmood T, Ali Z, Gumaei A (2021) Interdependency of complex fuzzy neighborhood operators and derived complex fuzzy coverings. IEEE Access 9:73506\u201373521","journal-title":"IEEE Access"},{"issue":"1","key":"1331_CR9","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1063\/1.4757515","volume":"1482","author":"AMDJS Alkouri","year":"2012","unstructured":"Alkouri AMDJS, Salleh AR (2012) Complex intuitionistic fuzzy sets. AIP Conf Proc Am Inst Phys 1482(1):464\u2013470","journal-title":"AIP Conf Proc Am Inst Phys"},{"issue":"10","key":"1331_CR10","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1002\/int.22127","volume":"34","author":"H Garg","year":"2019","unstructured":"Garg H, Rani D (2019) Some results on information measures for complex intuitionistic fuzzy sets. Int J Intell Syst 34(10):2319\u20132363","journal-title":"Int J Intell Syst"},{"issue":"16","key":"1331_CR11","doi-asserted-by":"publisher","first-page":"1922","DOI":"10.3390\/math9161922","volume":"9","author":"Z Ali","year":"2021","unstructured":"Ali Z, Mahmood T, Aslam M, Chinram R (2021) Another view of complex intuitionistic fuzzy soft sets based on prioritized aggregation operators and their applications to multiattribute decision making. Mathematics 9(16):1922","journal-title":"Mathematics"},{"issue":"3","key":"1331_CR12","first-page":"353","volume":"25","author":"B Schweizer","year":"1960","unstructured":"Schweizer B, Sklar A (1960) Probabilistic metric spaces. Clustering of interval data based on city-block distances. Pattern Recogn Lett 25(3):353\u2013365","journal-title":"Pattern Recogn Lett"},{"issue":"6","key":"1331_CR13","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1109\/3468.983429","volume":"31","author":"RR Yager","year":"2001","unstructured":"Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A 31(6):724\u2013731","journal-title":"IEEE Trans Syst Man Cybern Part A"},{"issue":"1","key":"1331_CR14","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1002\/int.21939","volume":"33","author":"W Jiang","year":"2018","unstructured":"Jiang W, Wei B, Liu X, Li X, Zheng H (2018) Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making. Int J Intell Syst 33(1):49\u201367","journal-title":"Int J Intell Syst"},{"issue":"6","key":"1331_CR15","doi-asserted-by":"publisher","DOI":"10.1111\/exsy.12325","volume":"35","author":"D Rani","year":"2018","unstructured":"Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making. Expert Syst 35(6):e12325","journal-title":"Expert Syst"},{"key":"1331_CR16","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/j.aej.2022.12.049","volume":"67","author":"H Garg","year":"2023","unstructured":"Garg H, Ali Z, Mahmood T, Ali MR, Alburaikan A (2023) Schweizer-Sklar prioritized aggregation operators for intuitionistic fuzzy information and their application in multi-attribute decision-making. Alex Eng J 67:229\u2013240","journal-title":"Alex Eng J"},{"key":"1331_CR17","doi-asserted-by":"crossref","unstructured":"Zhang L (2018) Intuitionistic fuzzy averaging Schweizer-Sklar operators based on interval-valued intuitionistic fuzzy numbers and its applications. In: 2018 Chinese Control and Decision Conference (CCDC)\u00a0(pp 2194\u20132197). IEEE","DOI":"10.1109\/CCDC.2018.8407490"},{"key":"1331_CR18","doi-asserted-by":"publisher","first-page":"26011","DOI":"10.1109\/ACCESS.2022.3156764","volume":"10","author":"A Hussain","year":"2022","unstructured":"Hussain A, Ullah K, Yang MS, Pamucar D (2022) Aczel-Alsina Aggregation Operators on T-Spherical Fuzzy (TSF) information with application to TSF multi-attribute decision making. IEEE Access 10:26011\u201326023","journal-title":"IEEE Access"},{"issue":"1","key":"1331_CR19","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s12652-021-02904-8","volume":"13","author":"\u015e \u00d6zl\u00fc","year":"2022","unstructured":"\u00d6zl\u00fc \u015e, Karaaslan F (2022) Correlation coefficient of T-spherical type-2 hesitant fuzzy sets and their applications in clustering analysis. J Ambient Intell Humaniz Comput 13(1):329\u2013357","journal-title":"J Ambient Intell Humaniz Comput"},{"issue":"7","key":"1331_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40314-022-01985-1","volume":"41","author":"M Javed","year":"2022","unstructured":"Javed M, Javeed S, Ullah K, Garg H, Pamucar D, Elmasry Y (2022) Approach to multi-attribute decision-making problems based on neutrality aggregation operators of T-spherical fuzzy information. Comput Appl Math 41(7):1\u201330","journal-title":"Comput Appl Math"},{"issue":"1","key":"1331_CR21","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s40815-021-01109-7","volume":"24","author":"P Liu","year":"2022","unstructured":"Liu P, Wang D (2022) An extended taxonomy method based on normal T-spherical fuzzy numbers for multiple-attribute decision-making. Int J Fuzzy Syst 24(1):73\u201390","journal-title":"Int J Fuzzy Syst"},{"issue":"11","key":"1331_CR22","doi-asserted-by":"publisher","first-page":"7041","DOI":"10.1007\/s00521-018-3521-2","volume":"31","author":"T Mahmood","year":"2019","unstructured":"Mahmood T, Ullah K, Khan Q, Jan N (2019) An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 31(11):7041\u20137053","journal-title":"Neural Comput Appl"},{"issue":"1","key":"1331_CR23","first-page":"1","volume":"42","author":"A Cagri Tolga","year":"2022","unstructured":"Cagri Tolga A, Basar M (2022) The assessment of a smart system in hydroponic vertical farming via fuzzy MCDM methods. J Intell Fuzzy Syst 42(1):1\u201312","journal-title":"J Intell Fuzzy Syst"},{"key":"1331_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2022.108773","volume":"174","author":"M Deveci","year":"2022","unstructured":"Deveci M, Gokasar I, Castillo O, Daim T (2022) Evaluation of Metaverse integration of freight fluidity measurement alternatives using fuzzy Dombi EDAS model. Comput Ind Eng 174:108773","journal-title":"Comput Ind Eng"},{"key":"1331_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2019.103352","volume":"87","author":"AC Tolga","year":"2020","unstructured":"Tolga AC, Parlak IB, Castillo O (2020) Finite-interval-valued Type-2 Gaussian fuzzy numbers applied to fuzzy TODIM in a healthcare problem. Eng Appl Artif Intell 87:103352","journal-title":"Eng Appl Artif Intell"},{"key":"1331_CR26","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.eswa.2019.01.054","volume":"124","author":"F Alali","year":"2019","unstructured":"Alali F, Tolga AC (2019) Portfolio allocation with the TODIM method. Expert Syst Appl 124:341\u2013348","journal-title":"Expert Syst Appl"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-01331-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-023-01331-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-01331-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T18:17:16Z","timestamp":1715883436000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-023-01331-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,20]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["1331"],"URL":"https:\/\/doi.org\/10.1007\/s40747-023-01331-w","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,20]]},"assertion":[{"value":"24 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}