{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T15:52:37Z","timestamp":1771689157275,"version":"3.50.1"},"reference-count":47,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,8,24]]},"abstract":"<jats:p>In comparison to intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), the Fermatean Fuzzy Set (FFS) is more efficacious in dealing ambiguous and imprecise data when making decisions. In this paper, we propose unique operations on Fermatean fuzzy information based on prioritized attributes, as well as Einstein\u2019s operations based on adjusting the priority of characteristics in the Fermatean fuzzy environment. We use Einstein\u2019s operations with prioritized attributes to propose new operations on Fermatean fuzzy numbers (FFNs), and then introduce basic aspects of these operations. Motivated by Einstein operations on FFNs, we develop Fermatean fuzzy Einstein prioritized arithmetic and geometric aggregation operators (AOs). In the first place, the concepts of a Fermatean fuzzy Einstein prioritized average (FFEPA), Fermatean fuzzy Einstein prioritized weighted average (FFEPWA), and Fermatean fuzzy Einstein prioritized ordered weighted average (FFEPOWA)-operators are introduced. Then, Fermatean fuzzy Einstein prioritized geometric (FFEPG) operator, Fermatean fuzzy Einstein prioritized weighted geometric (FFEPWG) operator, Fermatean fuzzy Einstein prioritized ordered weighted geometric (FFEPOWG) operator, and Fermatean fuzzy Einstein hybrid geometric (FFEHG) operator are given. We also go through some of the key characteristics of these operators. Moreover, using these operators, we establish algorithm for addressing a multiple attribute decision-making issue using Fermatean fuzzy data and attribute prioritizing. The case of university faculty selection is taken as a scenario to analyze and demonstrate the applicability of our suggested model. In addition, a comparison of the proposed and current operators is conducted, and the impact of attribute priority on the ranking order of alternatives is explored.<\/jats:p>","DOI":"10.3233\/jifs-230681","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T11:20:09Z","timestamp":1687260009000},"page":"3985-4008","source":"Crossref","is-referenced-by-count":7,"title":["University\u2019s recruitment process using Fermatean fuzzy Einstein prioritized aggregation operators"],"prefix":"10.1177","volume":"45","author":[{"given":"Omar M.","family":"Barokab","sequence":"first","affiliation":[{"name":"Faculty of Computing and Information Technology, P.O. Box 411, King Abdulaziz University, Rabigh, Jeddah, Saudi Arabia"}]},{"given":"Asghar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan"}]},{"given":"Sher Afzal","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Computer Sciences, Abdul Wali Khan University, Mardan, KP, Pakistan"}]},{"given":"Young Bae","family":"Jun","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Gyeongsang National University, Jinju, Korea"}]},{"given":"Ali Muhammad Ali","family":"Rushdi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, King Abdulaziz University, Jeddah, Saudi Arabia"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/JIFS-230681_ref1","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1002\/int.22062","article-title":"Spherical aggregation operators and theirapplication in multi attribute group decision-making","volume":"34","author":"Ashraf","year":"2019","journal-title":"International Journal of Intelligent Systems"},{"issue":"6","key":"10.3233\/JIFS-230681_ref2","doi-asserted-by":"crossref","first-page":"6102","DOI":"10.3233\/JIFS-181941","article-title":"Sphericalfuzzy sets and its representation of spherical fuzzy t-norms and t-conorms","volume":"36","author":"Ashraf","year":"2019","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"10.3233\/JIFS-230681_ref3","first-page":"1","article-title":"Spherical fuzzy Dombi aggregation operators and their application in group decision makingproblems","author":"Ashraf","year":"2019","journal-title":"Journal of Ambient Intelligence and Humanized Computing"},{"issue":"1","key":"10.3233\/JIFS-230681_ref4","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.2991\/ijcis.d.200908.001","article-title":"Multi-criteria group decision-making using spherical fuzzy prioritized weighted aggregation operators","volume":"13","author":"Akram","year":"2020","journal-title":"International Journal of Computational Intelligence Systems"},{"key":"10.3233\/JIFS-230681_ref5","first-page":"1","article-title":"Decision aid modeling based on sine trigonometric spherical fuzzy aggregation information","author":"Ashraf","year":"2021","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-230681_ref6","first-page":"1","article-title":"Emergency decision support modeling under generalized spherical fuzzy Einstein aggregation information","author":"Ashraf","year":"2021","journal-title":"Journal of Ambient Intelligence and Humanized Computing"},{"key":"10.3233\/JIFS-230681_ref7","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy sets and Systems"},{"key":"10.3233\/JIFS-230681_ref8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-7908-1870-3","volume-title":"Intuitionistic fuzzysets","author":"Atanassov","year":"1999"},{"issue":"2","key":"10.3233\/JIFS-230681_ref9","first-page":"176","article-title":"Interval-valued fermatean neutrosophicgraphs","volume":"5","author":"Broumi","year":"2022","journal-title":"Decision Making: Applications in Management andEngineering"},{"issue":"1","key":"10.3233\/JIFS-230681_ref10","doi-asserted-by":"crossref","first-page":"105","DOI":"10.31181\/rme2001020105t","article-title":"Einstein geometric aggregation operators using a novel complex interval-valued pythagorean fuzzy setting with application in green supplier chain management","volume":"2","author":"Ali","year":"2021","journal-title":"Reports in Mechanical Engineering"},{"key":"10.3233\/JIFS-230681_ref11","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ins.2016.02.049","article-title":"Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators","volume":"352","author":"Chen","year":"2016","journal-title":"Information Sciences"},{"issue":"2","key":"10.3233\/JIFS-230681_ref12","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0165-0114(98)00235-8","article-title":"An application of intuitionistic fuzzy sets in medical diagnosis","volume":"117","author":"De","year":"2001","journal-title":"Fuzzy sets and Systems"},{"issue":"2","key":"10.3233\/JIFS-230681_ref13","doi-asserted-by":"crossref","first-page":"399","DOI":"10.22190\/FUME220223013Z","article-title":"Risk priority evaluation of power transformer parts based on hybrid FMEA framework under hesitant fuzzy environment","volume":"20","author":"Zhou","year":"2022","journal-title":"Facta Universitatis-Series: Mechanical Engineering"},{"issue":"1","key":"10.3233\/JIFS-230681_ref14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/TFUZZ.2003.822678","article-title":"On the representation of intuitionistic fuzzy t-norms and t-conorms","volume":"12","author":"Deschrijver","year":"2004","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-230681_ref15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.17485\/ijst\/2016\/v9i30\/97528","article-title":"Intuitionistic fuzzy genetic weighted averaging operator and its application for multiple attribute decision making in E-learning","volume":"9","author":"Goyal","year":"2016","journal-title":"Indian Journal of Science and Technology"},{"issue":"1","key":"10.3233\/JIFS-230681_ref16","doi-asserted-by":"crossref","first-page":"283","DOI":"10.3934\/jimo.2017047","article-title":"Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process","volume":"14","author":"Garg","year":"2018","journal-title":"Journal of Industrial & Management Optimization"},{"issue":"15","key":"10.3233\/JIFS-230681_ref17","doi-asserted-by":"crossref","first-page":"4959","DOI":"10.1007\/s00500-018-3202-1","article-title":"An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theoryand their application in decision making","volume":"22","author":"Garg","year":"2018","journal-title":"Soft Computing"},{"issue":"9","key":"10.3233\/JIFS-230681_ref18","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1002\/int.21809","article-title":"A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making","volume":"31","author":"Garg","year":"2016","journal-title":"International Journal of Intelligent Systems"},{"key":"10.3233\/JIFS-230681_ref19","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.cie.2016.08.017","article-title":"Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making","volume":"101","author":"Garg","year":"2016","journal-title":"Computers & Industrial Engineering"},{"issue":"6","key":"10.3233\/JIFS-230681_ref20","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1002\/int.21860","article-title":"Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process","volume":"32","author":"Garg","year":"2017","journal-title":"International Journal of Intelligent Systems"},{"issue":"6","key":"10.3233\/JIFS-230681_ref21","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1080\/0952813X.2018.1467497","article-title":"Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making","volume":"30","author":"Garg","year":"2018","journal-title":"Journal of Experimental &Theoretical Artificial Intelligence"},{"issue":"3","key":"10.3233\/JIFS-230681_ref22","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1002\/int.21966","article-title":"New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making","volume":"33","author":"Garg","year":"2018","journal-title":"International Journal of Intelligent Systems"},{"key":"10.3233\/JIFS-230681_ref23","first-page":"276","article-title":"Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione Trappl","volume":"3","author":"Hamachar","year":"1978","journal-title":"Progress in Cybernatics and Systems Research"},{"issue":"3","key":"10.3233\/JIFS-230681_ref24","doi-asserted-by":"crossref","first-page":"447","DOI":"10.22190\/FUME210318047B","article-title":"Dnumbers - FUCOM \u2013 Fuzzy RAFSI model for selecting the group of construction machines for enabling mobility","volume":"19","author":"Bozanic","year":"2021","journal-title":"Facta Universitatis-Series Mechanical Engineering"},{"issue":"1","key":"10.3233\/JIFS-230681_ref25","doi-asserted-by":"crossref","first-page":"505","DOI":"10.3233\/IFS-131019","article-title":"Intuitionistic fuzzy Hamacher aggregation operators andtheir application to multiple attribute decision making","volume":"27","author":"Huang","year":"2014","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"10.3233\/JIFS-230681_ref26","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.asoc.2018.10.021","article-title":"Picture fuzzy Dombi aggregation operators: Application to MADM process","volume":"74","author":"Jana","year":"2019","journal-title":"Applied Soft Computing"},{"issue":"1","key":"10.3233\/JIFS-230681_ref27","doi-asserted-by":"crossref","first-page":"75","DOI":"10.3390\/sym11010075","article-title":"Assessment of enterprise performance based onpicture fuzzy Hamacher aggregation operators","volume":"11","author":"Jana","year":"2019","journal-title":"Symmetry"},{"issue":"5","key":"10.3233\/JIFS-230681_ref28","doi-asserted-by":"crossref","first-page":"413","DOI":"10.3390\/math7050413","article-title":"Linguistic spherical fuzzy aggregation operators and their applications in multi-attribute decision making problems","volume":"7","author":"Jin","year":"2019","journal-title":"Mathematics"},{"issue":"7","key":"10.3233\/JIFS-230681_ref29","doi-asserted-by":"crossref","first-page":"608","DOI":"10.3390\/math7070608","article-title":"Logarithmic aggregation operators of picture fuzzy numbers for multi-attribute decision making problems","volume":"7","author":"Khan","year":"2019","journal-title":"Mathematics"},{"issue":"3","key":"10.3233\/JIFS-230681_ref30","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s40096-019-0291-7","article-title":"Picture fuzzy aggregationin formation based on Einstein operations and their application indecision making","volume":"13","author":"Khan","year":"2019","journal-title":"Mathematical Sciences"},{"issue":"1","key":"10.3233\/JIFS-230681_ref31","doi-asserted-by":"crossref","first-page":"65","DOI":"10.3390\/e20010065","article-title":"Multi-attribute decision-making based onBonferroni mean operators under cubic intuitionistic fuzzy set environment","volume":"20","author":"Kaur","year":"2018","journal-title":"Entropy"},{"key":"10.3233\/JIFS-230681_ref32","first-page":"1","article-title":"Multiple attribute decision-making based on cubical fuzzy aggregation operators","author":"Khan","year":"2021","journal-title":"Granular Computing"},{"issue":"1","key":"10.3233\/JIFS-230681_ref33","first-page":"43","article-title":"Intuitionistic fuzzy set vs. fuzzy setapplication in medical pattern recognition","volume":"47","author":"Khatibi","year":"2009","journal-title":"ArtificialIntelligence in Medicine"},{"issue":"5","key":"10.3233\/JIFS-230681_ref34","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1615\/Int.J.UncertaintyQuantification.2018020471","article-title":"Cubic intuitionistic fuzzy aggregation operators","volume":"8","author":"Kaur","year":"2018","journal-title":"International Journal for Uncertainty Quantification"},{"issue":"1","key":"10.3233\/JIFS-230681_ref35","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1007\/s40815-019-00726-7","article-title":"Utilizing linguistic picture fuzzy aggregation operators for multiple-attribute decision-making problems","volume":"22","author":"Qiyas","year":"2020","journal-title":"International Journal of Fuzzy Systems"},{"issue":"6","key":"10.3233\/JIFS-230681_ref36","doi-asserted-by":"crossref","first-page":"e12325","DOI":"10.1111\/exsy.12325","article-title":"Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making","volume":"35","author":"Rani","year":"2018","journal-title":"Expert Systems"},{"key":"10.3233\/JIFS-230681_ref37","doi-asserted-by":"crossref","first-page":"106037","DOI":"10.1016\/j.cie.2019.106037","article-title":"Weighted picture fuzzy aggregation operators and their applications tomulti-criteria decision-making problems","volume":"137","author":"Tian","year":"2019","journal-title":"Computers & Industrial Engineering"},{"issue":"5","key":"10.3233\/JIFS-230681_ref38","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TFUZZ.2012.2189405","article-title":"Intuitionistic fuzzy information aggregation using Einstein operations","volume":"20","author":"Wang","year":"2012","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"11","key":"10.3233\/JIFS-230681_ref39","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1002\/int.20498","article-title":"Intuitionistic fuzzy geometric aggregation operators based on Einstein operations","volume":"26","author":"Wang","year":"2011","journal-title":"International Journalof Intelligent Systems"},{"key":"10.3233\/JIFS-230681_ref40","first-page":"477","article-title":"Some geometric aggregation operators based on picture fuzzy sets and their application inmultiple attribute decision making","volume":"37","author":"Wang","year":"2017","journal-title":"Ital. J. Pure Appl. Math"},{"issue":"2","key":"10.3233\/JIFS-230681_ref41","doi-asserted-by":"crossref","first-page":"713","DOI":"10.3233\/JIFS-161798","article-title":"Picture fuzzy aggregation operators and their application to multiple attribute decision making","volume":"33","author":"Wei","year":"2017","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"19","key":"10.3233\/JIFS-230681_ref42","doi-asserted-by":"crossref","first-page":"3775","DOI":"10.1016\/j.ins.2008.06.008","article-title":"Clustering algorithm for intuitionistic fuzzy sets","volume":"178","author":"Xu","year":"2008","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-230681_ref43","doi-asserted-by":"crossref","unstructured":"Xu Z. and Cai X. , Intuitionistic fuzzy information aggregation, Springer, Berlin, Heidelberg, 2012.","DOI":"10.1007\/978-3-642-29584-3"},{"issue":"4","key":"10.3233\/JIFS-230681_ref44","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/03081070600574353","article-title":"Some geometric aggregation operators based on intuitionistic fuzzy sets","volume":"35","author":"Xu","year":"2006","journal-title":"International Journal of General Systems"},{"issue":"11","key":"10.3233\/JIFS-230681_ref45","doi-asserted-by":"crossref","first-page":"593","DOI":"10.3390\/sym10110593","article-title":"Some picture fuzzy Dombi Heronian mean operators with their application to multi-attributedecision-making","volume":"10","author":"Zhang","year":"2018","journal-title":"Symmetry"},{"key":"10.3233\/JIFS-230681_ref46","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.knosys.2012.09.006","article-title":"Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making","volume":"37","author":"Zhao","year":"2013","journal-title":"Knowledge Based Systems"},{"key":"10.3233\/JIFS-230681_ref47","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ijar.2007.08.009","article-title":"Prioritized aggregation operators","volume":"48","author":"Yager","year":"2008","journal-title":"Int. J.Approx. Reason."}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-230681","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T05:57:24Z","timestamp":1769666244000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-230681"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,24]]},"references-count":47,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/jifs-230681","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,24]]}}}