{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:20:05Z","timestamp":1776784805756,"version":"3.51.2"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T00:00:00Z","timestamp":1671062400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel\u2013Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel\u2013Alsina averaging (IFPAAA) and IF-prioritized Aczel\u2013Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators.<\/jats:p>","DOI":"10.3390\/sym14122655","type":"journal-article","created":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T02:16:41Z","timestamp":1671157001000},"page":"2655","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Prioritized Aggregation Operators for Intuitionistic Fuzzy Information Based on Aczel\u2013Alsina T-Norm and T-Conorm and Their Applications in Group Decision-Making"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0154-3199","authenticated-orcid":false,"given":"Mehwish","family":"Sarfraz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Riphah International University (Lahore Campus), Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1438-6413","authenticated-orcid":false,"given":"Kifayat","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University (Lahore Campus), Lahore 54000, Pakistan"}]},{"given":"Maria","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University (Lahore Campus), Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8522-1942","authenticated-orcid":false,"given":"Dragan","family":"Pamucar","sequence":"additional","affiliation":[{"name":"Department of Operations Research and Statistics, Faculty of Organizational Sciences, University of Belgrade, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9657-0889","authenticated-orcid":false,"given":"Darko","family":"Bo\u017eani\u0107","sequence":"additional","affiliation":[{"name":"Military Academy, University of Defense in Belgrade, 11000 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_2","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 Syst."},{"key":"ref_3","first-page":"27","article-title":"Symmetric Implicational Algorithm Derived from Intuitionistic Fuzzy Entropy","volume":"19","author":"Tang","year":"2022","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/TETCI.2017.2739128","article-title":"Computational Intelligence for Demand Response Exchange Considering Temporal Characteristics of Load Profile via Adaptive Fuzzy Inference System","volume":"2","author":"Panwar","year":"2018","journal-title":"IEEE Trans. Emerg. Top. Comput. Intell."},{"key":"ref_5","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 Trans. Fuzzy Syst."},{"key":"ref_6","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":"Int. J. Intell. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s00521-013-1499-3","article-title":"Learning the Optimal Parameter of the Hamacher T-Norm Applied for Fuzzy-Rule-Based Model Extraction","volume":"24","author":"Lovassy","year":"2014","journal-title":"Neural Comput. Applic"},{"key":"ref_8","unstructured":"De Baets, B., and De Meyer, H.E. (2001, January 5\u20137). The Frank T-Norm Family in Fuzzy Similarity Measurement. Proceedings of the EUSFLAT Conference, Leicester, UK."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0165-0114(82)90005-7","article-title":"A General Class of Fuzzy Operators, the DeMorgan Class of Fuzzy Operators and Fuzziness Measures Induced by Fuzzy Operators","volume":"8","author":"Dombi","year":"1982","journal-title":"Fuzzy Sets Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/BF02189626","article-title":"Characterizations of Some Classes of Quasilinear Functions with Applications to Triangular Norms and to Synthesizing Judgements","volume":"25","author":"Alsina","year":"1982","journal-title":"Aequ. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","article-title":"Intuitionistic Fuzzy Aggregation Operators","volume":"15","author":"Xu","year":"2007","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_12","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":"Int. J. Gen. Syst."},{"key":"ref_13","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":"Int. J. Intell. Syst."},{"key":"ref_14","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 Trans. Fuzzy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"505","DOI":"10.3233\/IFS-131019","article-title":"Intuitionistic Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making","volume":"27","author":"Huang","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2235","DOI":"10.3233\/IFS-151699","article-title":"Multiple Attribute Group Decision Making Methods Based on Intuitionistic Fuzzy Frank Power Aggregation Operators","volume":"29","author":"Zhang","year":"2015","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1002\/int.22684","article-title":"Aczel\u2013Alsina Aggregation Operators and Their Application to Intuitionistic Fuzzy Multiple Attribute Decision Making","volume":"37","author":"Senapati","year":"2022","journal-title":"Int. J. Intell. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hussain, A., Ullah, K., Alshahrani, M.N., Yang, M.-S., and Pamucar, D. (2022). Novel Aczel\u2013Alsina Operators for Pythagorean Fuzzy Sets with Application in Multi-Attribute Decision Making. Symmetry, 14.","DOI":"10.3390\/sym14050940"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Khan, M.R., Wang, H., Ullah, K., and Karamti, H. (2022). Construction Material Selection by Using Multi-Attribute Decision Making Based on q-Rung Orthopair Fuzzy Aczel\u2013Alsina Aggregation Operators. Appl. Sci., 12.","DOI":"10.3390\/app12178537"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"26011","DOI":"10.1109\/ACCESS.2022.3156764","article-title":"Aczel-Alsina Aggregation Operators on T-Spherical Fuzzy (TSF) Information with Application to TSF Multi-Attribute Decision Making","volume":"10","author":"Hussain","year":"2022","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40314-021-01742-w","article-title":"Approaches to Multi-Attribute Decision-Making Based on Picture Fuzzy Aczel\u2013Alsina Average Aggregation Operators","volume":"41","author":"Senapati","year":"2022","journal-title":"Comput. Appl. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5059","DOI":"10.1002\/int.22751","article-title":"Novel Aczel\u2013Alsina Operations-Based Interval-Valued Intuitionistic Fuzzy Aggregation Operators and Their Applications in Multiple Attribute Decision-Making Process","volume":"37","author":"Senapati","year":"2021","journal-title":"Int. J. Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1080\/03081079.2022.2036140","article-title":"Novel Aczel\u2013Alsina Operations-Based Hesitant Fuzzy Aggregation Operators and Their Applications in Cyclone Disaster Assessment","volume":"51","author":"Senapati","year":"2022","journal-title":"Int. J. Gen. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1098631","DOI":"10.1155\/2021\/1098631","article-title":"Picture Fuzzy Maclaurin Symmetric Mean Operators and Their Applications in Solving Multiattribute Decision-Making Problems","volume":"2021","author":"Ullah","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9097","DOI":"10.1007\/s00500-021-05829-8","article-title":"Applications of Improved Spherical Fuzzy Dombi Aggregation Operators in Decision Support System","volume":"25","author":"Khan","year":"2021","journal-title":"Soft Comput."},{"key":"ref_26","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."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s10700-009-9063-4","article-title":"Prioritized OWA Aggregation","volume":"8","author":"Yager","year":"2009","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1016\/j.eswa.2010.07.039","article-title":"On Prioritized Weighted Aggregation in Multi-Criteria Decision Making","volume":"38","author":"Yan","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.inffus.2012.01.011","article-title":"Prioritized Intuitionistic Fuzzy Aggregation Operators","volume":"14","author":"Yu","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ali, Z., Mahmood, T., Aslam, M., and 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.","DOI":"10.3390\/math9161922"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s40314-019-0764-1","article-title":"Group Decision-Making Method Based on Prioritized Linguistic Intuitionistic Fuzzy Aggregation Operators and Its Fundamental Properties","volume":"38","author":"Arora","year":"2019","journal-title":"Comp. Appl. Math."},{"key":"ref_32","first-page":"466","article-title":"Prioritized Averaging\/Geometric Aggregation Operators under the Intuitionistic Fuzzy Soft Set Environment","volume":"25","author":"Arora","year":"2017","journal-title":"Sci. Iran."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.ins.2014.05.018","article-title":"A Prioritized Aggregation Operator-Based Approach to Multiple Criteria Decision Making Using Interval-Valued Intuitionistic Fuzzy Sets: A Comparative Perspective","volume":"281","author":"Chen","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2229","DOI":"10.3233\/JIFS-172262","article-title":"Pythagorean Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making","volume":"35","author":"Gao","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3631","DOI":"10.1007\/s00500-019-04130-z","article-title":"Bipolar Fuzzy Dombi Prioritized Aggregation Operators in Multiple Attribute Decision Making","volume":"24","author":"Jana","year":"2020","journal-title":"Soft. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Riaz, M., Pamucar, D., Athar Farid, H.M., and Hashmi, M.R. (2020). Q-Rung Orthopair Fuzzy Prioritized Aggregation Operators and Their Application towards Green Supplier Chain Management. Symmetry, 12.","DOI":"10.3390\/sym12060976"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"11508","DOI":"10.1109\/ACCESS.2017.2784963","article-title":"Dual Hesitant Bipolar Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making","volume":"6","author":"Gao","year":"2018","journal-title":"IEEE Access"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7469","DOI":"10.3233\/JIFS-200789","article-title":"Extensions of Prioritized Weighted Aggregation Operators for Decision-Making under Complex q-Rung Orthopair Fuzzy Information","volume":"39","author":"Liu","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.knosys.2012.03.011","article-title":"Hesitant Fuzzy Prioritized Operators and Their Application to Multiple Attribute Decision Making","volume":"31","author":"Wei","year":"2012","journal-title":"Knowl.-Based Syst."},{"key":"ref_40","first-page":"104","article-title":"Prioritized Muirhead Mean Aggregation Operators under the Complex Single-Valued Neutrosophic Settings and Their Application in Multi-Attribute Decision Making","volume":"1","author":"Mahmood","year":"2022","journal-title":"J. Comput. Cogn. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4659","DOI":"10.1002\/int.22474","article-title":"Generalized MULTIMOORA Method and Dombi Prioritized Weighted Aggregation Operators Based on T-Spherical Fuzzy Sets and Their Applications","volume":"36","author":"Mahmood","year":"2021","journal-title":"Int. J. Intell. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4690808","DOI":"10.1155\/2020\/4690808","article-title":"A Novel Approach towards Bipolar Soft Sets and Their Applications","volume":"2020","author":"Mahmood","year":"2020","journal-title":"J. Math."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"33","DOI":"10.5121\/ijfls.2012.2303","article-title":"Comparison of Different T-Norm Operators in Classification Problems","volume":"2","author":"Farahbod","year":"2012","journal-title":"Int. J. Fuzzy Log. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s41066-019-00209-y","article-title":"Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Multiple Attribute Decision-Making","volume":"6","author":"Seikh","year":"2021","journal-title":"Granul. Comput."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Waqar, M., Ullah, K., Pamucar, D., Jovanov, G., and Vranje\u0161, \u00d0. (2022). An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators. Energies, 15.","DOI":"10.3390\/en15113939"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Ali, Z., Mahmood, T., Ullah, K., Pamucar, D., and Cirovic, G. (2021). Power Aggregation Operators Based on T-Norm and t-Conorm under the Complex Intuitionistic Fuzzy Soft Settings and Their Application in Multi-Attribute Decision Making. Symmetry, 13.","DOI":"10.3390\/sym13111986"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.3233\/JIFS-210352","article-title":"An Approach to Decision Making with Interval-Valued Complex Pythagorean Fuzzy Model for Evaluating Personal Risk of Mental Patients","volume":"41","author":"Wang","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Liu, P., Mahmood, T., and Ali, Z. (2020). Complex Q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making. Information, 11.","DOI":"10.3390\/info11010005"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"7041","DOI":"10.1007\/s00521-018-3521-2","article-title":"An Approach toward Decision-Making and Medical Diagnosis Problems Using the Concept of Spherical Fuzzy Sets","volume":"31","author":"Mahmood","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Akram, M., Ullah, K., and Pamucar, D. (2022). Performance Evaluation of Solar Energy Cells Using the Interval-Valued T-Spherical Fuzzy Bonferroni Mean Operators. Energies, 15.","DOI":"10.3390\/en15010292"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2655\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:42:02Z","timestamp":1760146922000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,15]]},"references-count":50,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["sym14122655"],"URL":"https:\/\/doi.org\/10.3390\/sym14122655","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,15]]}}}