{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T02:30:50Z","timestamp":1770690650682,"version":"3.49.0"},"reference-count":56,"publisher":"Emerald","issue":"4","license":[{"start":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T00:00:00Z","timestamp":1644364800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJICC"],"published-print":{"date-parts":[[2022,9,22]]},"abstract":"Purpose<\/jats:title>The authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined. Further, based on these operators, a decision-making approach is presented under the Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.<\/jats:p><\/jats:sec>Design\/methodology\/approach<\/jats:title>In real-world situations, Pythagorean fuzzy numbers are exceptionally useful for representing ambiguous data. The authors look at multi-criteria decision-making issues in which the parameters have a prioritization relationship. The idea of a priority degree is introduced. The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.<\/jats:p><\/jats:sec>Findings<\/jats:title>The authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined. Further, based on these operators, a decision-making approach is presented under the Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.<\/jats:p><\/jats:sec>Originality\/value<\/jats:title>The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined.<\/jats:p><\/jats:sec>","DOI":"10.1108\/ijicc-10-2021-0224","type":"journal-article","created":{"date-parts":[[2022,2,8]],"date-time":"2022-02-08T05:50:52Z","timestamp":1644299452000},"page":"510-539","source":"Crossref","is-referenced-by-count":14,"title":["Pythagorean fuzzy prioritized aggregation operators with priority degrees for multi-criteria decision-making"],"prefix":"10.1108","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8318-0750","authenticated-orcid":false,"given":"Hafiz Muhammad Athar","family":"Farid","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8115-9168","authenticated-orcid":false,"given":"Muhammad","family":"Riaz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2022,2,9]]},"reference":[{"key":"key2022092105490411000_ref001","doi-asserted-by":"crossref","first-page":"10309","DOI":"10.1007\/s00500-021-05771-9","article-title":"Group decision-making framework under linguistic q-rung orthopair fuzzy Einstein models","volume":"25","year":"2021","journal-title":"Soft Computing"},{"issue":"1","key":"key2022092105490411000_ref002","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","year":"1986","journal-title":"Fuzzy Sets and Systems"},{"key":"key2022092105490411000_ref003","doi-asserted-by":"publisher","DOI":"10.1108\/K-11-2020-0747","article-title":"Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making","year":"2021","journal-title":"Kybernetes"},{"key":"key2022092105490411000_ref004","article-title":"Sustainable building material selection: an integrated multi-criteria large group decision making framework","volume":"113","year":"2021","journal-title":"Applied Soft Computing"},{"key":"key2022092105490411000_ref005","article-title":"Expertise-based bid evaluation for construction-contractor selection with generalized comparative linguistic ELECTRE III","volume":"125","year":"2021","journal-title":"Automation in Construction"},{"key":"key2022092105490411000_ref006","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.inffus.2020.11.010","article-title":"Online-review analysis based large-scale group decision-making for determining passenger demands and evaluating passenger satisfaction: case study of high-speed rail system in China","volume":"69","year":"2021","journal-title":"Information Fusion"},{"issue":"12","key":"key2022092105490411000_ref007","doi-asserted-by":"publisher","first-page":"7239","DOI":"10.1002\/int.22587","article-title":"Some generalized q-rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws","volume":"36","year":"2021","journal-title":"International Journal of Intelligent Systems"},{"issue":"3","key":"key2022092105490411000_ref008","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/TFUZZ.2018.2860967","article-title":"Another view on generalized intuitionistic fuzzy soft sets and related multi-attribute decision making methods","volume":"27","year":"2019","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"key2022092105490411000_ref009","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1007\/s10588-017-9242-8","article-title":"Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process","volume":"23","year":"2017","journal-title":"Computational and Mathematical Organization Theory"},{"key":"key2022092105490411000_ref010","article-title":"Multi-criteria decision-making method based on prioritized muirhead mean aggregation operator under neutrosophic set environment","volume":"10","year":"2018","journal-title":"Symmetry"},{"issue":"5","key":"key2022092105490411000_ref011","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.3934\/jimo.2020069","article-title":"Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers","volume":"17","year":"2021","journal-title":"Journal of Industrial and Management Optimization"},{"key":"key2022092105490411000_ref012","doi-asserted-by":"crossref","first-page":"4373","DOI":"10.1007\/s10115-020-01491-y","article-title":"Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: its application in multicriteria decision making process","volume":"62","year":"2020","journal-title":"Knowledge and Information Systems"},{"key":"key2022092105490411000_ref013","article-title":"Linear Diophantine fuzzy Einstein aggregation operators for multi-criteria decision-making problems","volume":"2021","year":"2021","journal-title":"Journal of Mathematics"},{"issue":"1","key":"key2022092105490411000_ref014","first-page":"40","article-title":"Aggregation operators, score function and accuracy function for multi criteria decision making in intuitionistic fuzzy context","volume":"20","year":"2014","journal-title":"Notes on Intuitionistic Fuzzy Sets"},{"key":"key2022092105490411000_ref015","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s41066-018-0093-6","article-title":"Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making","volume":"4","year":"2019","journal-title":"Granular Computing"},{"issue":"1","key":"key2022092105490411000_ref016","first-page":"1","article-title":"Novel generalized simplified neutrosophic number Einstein aggregation operator","volume":"48","year":"2018","journal-title":"International Journal of Applied Mathematics"},{"issue":"9","key":"key2022092105490411000_ref017","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1002\/int.22123","article-title":"Prioritized aggregation operators based on the priority degrees in multicriteria decision-making","volume":"34","year":"2019","journal-title":"International Journal of Intelligent Systems"},{"issue":"5","key":"key2022092105490411000_ref018","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1080\/0952813X.2019.1694589","article-title":"Interval-valued pythagorean fuzzy power average-based MULTIMOORA method for multi-criteria decision-making","volume":"32","year":"2020","journal-title":"Journal of Experimental and Theoretical Artificial Intelligence"},{"key":"key2022092105490411000_ref019","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s40747-020-00261-1","article-title":"Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis","volume":"7","year":"2021","journal-title":"Complex and Intelligent Systems"},{"issue":"2","key":"key2022092105490411000_ref020","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1108\/IJICC-06-2020-0067","article-title":"Bibliometric analysis on Pythagorean fuzzy sets during 2013\u20132020","volume":"14","year":"2021","journal-title":"International Journal of Intelligent Computing and Cybernetics"},{"key":"key2022092105490411000_ref021","article-title":"TOPSIS method based on correlation coefficient and entropy measure for linguistic pythagorean fuzzy sets and its application to multiple attribute decision making","volume":"2019","year":"2019","journal-title":"Complexity"},{"issue":"5","key":"key2022092105490411000_ref022","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/s40815-016-0195-8","article-title":"The aggregation operators based on Archimedean t-conorm and t-norm for single-valued neutrosophic numbers and their application to decision making","volume":"18","year":"2016","journal-title":"International Journal of Fuzzy System"},{"key":"key2022092105490411000_ref023","first-page":"242","article-title":"Some generalized neutrosophic number hamacher aggregation operators and their application to group decision making","volume":"16","year":"2014","journal-title":"International Journal of Fuzzy Systems"},{"issue":"2","key":"key2022092105490411000_ref024","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1002\/int.21933","article-title":"Some q-rung orthopair fuzzy Bonferroni mean operators and their application to multi-attribute group decision making","volume":"33","year":"2018","journal-title":"International Journal of Intelligent System"},{"issue":"6","key":"key2022092105490411000_ref025","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1080\/0952813X.2017.1310309","article-title":"Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making","volume":"29","year":"2017","journal-title":"Journal of Experimental and Theoretical Artificial Intelligence"},{"issue":"12","key":"key2022092105490411000_ref026","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.1002\/int.22032","article-title":"Multiple attribute group decision making based on q-rung orthopair fuzzy Heronianmean operators","volume":"33","year":"2018","journal-title":"International Journal of Intelligent System"},{"issue":"1","key":"key2022092105490411000_ref027","first-page":"31","article-title":"Some generalized aggregation operators for cubic hesitant fuzzy sets and their application to multi-criteria decision making","volume":"49","year":"2017","journal-title":"Punjab University Journal of Mathematics"},{"key":"key2022092105490411000_ref028","doi-asserted-by":"publisher","DOI":"10.1108\/IJICC-06-2021-0128","article-title":"Knowledge diffusion trajectories in the Pythagorean fuzzy field based on main path analysis","volume":"14","year":"2021","journal-title":"International Journal of Intelligent Computing and Cybernetics"},{"key":"key2022092105490411000_ref029","article-title":"Novel approach to multi-attribute group decision-making based on interval-valued Pythagorean fuzzy power Maclaurin symmetric mean operator","volume":"155","year":"2021","journal-title":"Computers and Industrial Engineering"},{"key":"key2022092105490411000_ref030","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1615\/Int.J.UncertaintyQuantification.2016018603","article-title":"Novel single-valued neutrosophic decision making operators under Frank norm operations and its application","volume":"6","year":"2016","journal-title":"International Journal for Uncertainty Quantification"},{"key":"key2022092105490411000_ref031","doi-asserted-by":"crossref","first-page":"2342","DOI":"10.1080\/00207721.2014.994050","article-title":"Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems","volume":"47","year":"2016","journal-title":"International Journal of Systems Science"},{"issue":"4","key":"key2022092105490411000_ref032","doi-asserted-by":"crossref","first-page":"415","DOI":"10.3233\/FI-2016-1415","article-title":"Fundamental properties of Pythagorean fuzzy aggregation operators","volume":"147","year":"2016","journal-title":"Fundamenta Informaticae"},{"issue":"4","key":"key2022092105490411000_ref033","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1108\/IJICC-06-2020-0064","article-title":"Concept of Yager operators with the picture fuzzy set environment and its application to emergency program selection","volume":"13","year":"2020","journal-title":"International Journal of Intelligent Computing and Cybernetics"},{"issue":"9","key":"key2022092105490411000_ref034","first-page":"174","article-title":"Approaches to Pythagorean fuzzy geometric aggregation operators","volume":"14","year":"2016","journal-title":"International Journal of Computer Science and Information Security"},{"key":"key2022092105490411000_ref035","article-title":"Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making","volume":"35","year":"2018","journal-title":"Expert Systems"},{"issue":"2","key":"key2022092105490411000_ref036","doi-asserted-by":"publisher","first-page":"4109","DOI":"10.3233\/JIFS-210506","article-title":"Novel q-rung orthopair fuzzy interaction aggregation operators and their application to low-carbon green supply chain management","volume":"41","year":"2021","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"7","key":"key2022092105490411000_ref037","article-title":"Novel approach for third-party reverse logistic provider selection process under linear Diophantine fuzzy prioritized aggregation operators","volume":"13","year":"2021","journal-title":"Symmetry"},{"issue":"6","key":"key2022092105490411000_ref038","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1080\/0952813X.2019.1694592","article-title":"Some power Heronian mean operators in multiple attribute decision-making based on q-rung orthopair hesitant fuzzy environment","volume":"32","year":"2020","journal-title":"Journal of Experimental and Theoretical Artificial Intelligence"},{"issue":"1","key":"key2022092105490411000_ref039","first-page":"503","article-title":"Algorithm for multiple attribute decision-making with interactive Archimedean norm operations under Pythagorean fuzzy uncertainty","volume":"14","year":"2021","journal-title":"International Journal of Computational Intelligence Systems"},{"key":"key2022092105490411000_ref040","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1007\/s00500-020-05193-z","article-title":"Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight","volume":"25","year":"2021","journal-title":"Soft Computing"},{"key":"key2022092105490411000_ref041","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TFUZZ.2012.2189405","article-title":"Intuitionistic fuzzy information aggregation using Einstein operators","volume":"20","year":"2012","journal-title":"IEEE Transections on Fuzzy Systems"},{"issue":"1","key":"key2022092105490411000_ref042","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/int.21946","article-title":"Pythagorean fuzzy power aggregation operators in multiple attribute decision making","volume":"33","year":"2018","journal-title":"International Journal of Intelligent Systems"},{"issue":"3","key":"key2022092105490411000_ref043","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.3233\/IFS-130806","article-title":"Hesitant triangular fuzzy information aggregation in multiple attribute decision making","volume":"26","year":"2014","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"2","key":"key2022092105490411000_ref044","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.3233\/JIFS-171741","article-title":"Some single-valued neutrosophic Dombi prioritized weighted aggregation operators in multiple attribute decision making","volume":"35","year":"2018","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"3","key":"key2022092105490411000_ref045","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3233\/KES-170363","article-title":"Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making","volume":"21","year":"2017","journal-title":"International Journal of Knowledge-Based and Intelligent Engineering Systems"},{"key":"key2022092105490411000_ref046","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","article-title":"Intuitionistic fuzzy aggregation operators","volume":"15","year":"2007","journal-title":"IEEE Transections on Fuzzy Systems"},{"key":"key2022092105490411000_ref047","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.knosys.2010.04.010","article-title":"Induced generalized intuitionitic fuzzy operators","volume":"24","year":"2011","journal-title":"Knowledge-based System"},{"key":"key2022092105490411000_ref048","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/03081070600574353","article-title":"Some geometric aggregation operators based on intuitionistic fuzzy sets","volume":"35","year":"2006","journal-title":"International Journal of General Systems"},{"key":"key2022092105490411000_ref049","first-page":"57","article-title":"Pythagorean fuzzy subsets","year":"2013"},{"key":"key2022092105490411000_ref050","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","article-title":"Pythagorean membership grades in multi criteria decision-making","volume":"22","year":"2014","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"key2022092105490411000_ref051","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ijar.2007.08.009","article-title":"Prioritized aggregation operators","volume":"48","year":"2008","journal-title":"International Journal of Approximate Reasoning"},{"key":"key2022092105490411000_ref052","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1002\/int.21584","article-title":"Pythagorean membership grades, complex numbers, and decision making","volume":"28","year":"2013","journal-title":"International Journal of Intelligent Systems"},{"key":"key2022092105490411000_ref053","doi-asserted-by":"crossref","first-page":"2459","DOI":"10.3233\/IFS-130916","article-title":"A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets","volume":"26","year":"2014","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"key2022092105490411000_ref054","article-title":"A novel multi-attribute decision-making method based on fuzzy rough sets","volume":"155","year":"2021","journal-title":"Computers and Industrial Engineering"},{"key":"key2022092105490411000_ref055","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","year":"1965","journal-title":"Information and Control"},{"key":"key2022092105490411000_ref056","article-title":"Interval neutrosophic sets and their application in multicriteria decision making problems","volume":"2014","year":"2014","journal-title":"The Scientific World Journal"}],"container-title":["International Journal of Intelligent Computing and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IJICC-10-2021-0224\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IJICC-10-2021-0224\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T22:55:00Z","timestamp":1753397700000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/ijicc\/article\/15\/4\/510-539\/126214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,9]]},"references-count":56,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,2,9]]},"published-print":{"date-parts":[[2022,9,22]]}},"alternative-id":["10.1108\/IJICC-10-2021-0224"],"URL":"https:\/\/doi.org\/10.1108\/ijicc-10-2021-0224","relation":{},"ISSN":["1756-378X"],"issn-type":[{"value":"1756-378X","type":"print"}],"subject":[],"published":{"date-parts":[[2022,2,9]]}}}