{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:43:56Z","timestamp":1760035436994,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T00:00:00Z","timestamp":1752105600000},"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>Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper is to provide the concept of Dombi t-norm (Dtn)- and Dombi t-conorm (Dtcn)-based accumulation operators on the class of TpVFFN, emphasizing how they behave symmetrically in aggregation processes to maintain consistency and fairness. To use s to illustrate mathematical circumstances, we first create a trapezoidal-valued fermatean fuzzy Dombi\u2019s weighted geometric operator, hexagonal hybird geometric operator, fermatean fuzzy order weighted geometric operator. Second, we use a multi-attribute group decision-making (MAGDM) approach to compute the recommended accumulation operators. Finally, we demonstrate the potential practical application of the proposed decision-making problem related to the pink cab.<\/jats:p>","DOI":"10.3390\/sym17071114","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T15:36:58Z","timestamp":1752161818000},"page":"1114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometric Accumulation Operators of Dombi Weighted Trapezoidal-Valued Fermatean Fuzzy Numbers with Multi-Attribute Group Decision Making"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4709-1857","authenticated-orcid":false,"given":"M.","family":"Kaviyarasu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Avadi, Chennai 600062, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-8089-4772","authenticated-orcid":false,"given":"J.","family":"Angel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Avadi, Chennai 600062, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6696-7287","authenticated-orcid":false,"given":"Mohammed","family":"Alqahtani","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, P.O. Box 93499, Riyadh 11673, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,10]]},"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","unstructured":"Smarandache, F. (1999). A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press."},{"key":"ref_4","first-page":"247","article-title":"An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers","volume":"28","author":"Ye","year":"2015","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_5","first-page":"63","article-title":"An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic set","volume":"1","author":"Chi","year":"2013","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106026","DOI":"10.1016\/j.engappai.2023.106026","article-title":"Information measures based on similarity under neutrosophic fuzzy environment and multi-criteria decision problems","volume":"122","author":"Bui","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ali, M., Hussain, Z., and Yang, M.-S. (2022). Hausdorff distance and similarity measures for single-valued neutrosophic sets with application in multi-criteria decision making. Electronics, 12.","DOI":"10.3390\/electronics12010201"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1057\/s41274-017-0190-y","article-title":"Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making","volume":"69","author":"Liu","year":"2018","journal-title":"J. Oper. Res. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s41066-019-00209-y","article-title":"Intuitionistic fuzzy Dombi accumulation Operators and their application to multiple attribute decision-making","volume":"6","author":"Seikh","year":"2021","journal-title":"Granul. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Shi, L., and Ye, J. (2018). Dombi Aggregation Operators of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making. Algorithms, 11.","DOI":"10.3390\/a11030029"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5163","DOI":"10.1007\/s10462-021-10017-z","article-title":"Improved q-rung orthopair fuzzy line integral accumulation Operators and their applications for multiple attribute decision making","volume":"54","author":"Shao","year":"2021","journal-title":"Artif. Intell. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108773","DOI":"10.1016\/j.cie.2022.108773","article-title":"Evaluation of metaverse integration of freight fluidity measurement alternatives using fuzzy Dombi EDAS model","volume":"174","author":"Deveci","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.asoc.2018.10.021","article-title":"Picture fuzzy Dombi accumulation Operators: Application to MADM process","volume":"74","author":"Jana","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"178","DOI":"10.31181\/sdmap21202524","article-title":"A comprehensive and systematic review of MCDM (MCDM) methods to solve decision-making problems: Two decades from 2004 to 2024","volume":"2","author":"Kumar","year":"2025","journal-title":"Spectr. Decis. Mak. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"80","DOI":"10.31181\/jdaic10006062023a","article-title":"An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws","volume":"3","author":"Ali","year":"2023","journal-title":"J. Decis. Anal. Intell. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"27","DOI":"10.31181\/sor2120258","article-title":"Hamacher accumulation Operators for Pythagorean fuzzy set and its application in multi-attribute decision-making problem","volume":"2","author":"Asif","year":"2025","journal-title":"Spectr. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"219","DOI":"10.31181\/sdmap21202525","article-title":"A review of MCDM applications to solve energy management problems from 2010\u20132025: Current state and future research","volume":"2","author":"Sahoo","year":"2025","journal-title":"Spectr. Decis. Mak. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"085203","DOI":"10.1088\/1402-4896\/ac7980","article-title":"A novel multi-criteria group decision-making method based on Aczel-Alsina spherical fuzzy accumulation operators: Application to evaluation of solar energy cells","volume":"97","author":"Naeem","year":"2022","journal-title":"Phys. Scr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1007\/s12652-020-02130-8","article-title":"Interval valued trapezoidal neutrosophic set: Multi-attribute decision making for prioritization of non-functional requirements","volume":"12","author":"Khatter","year":"2021","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00521-016-2673-1","article-title":"An improved ranking method for comparing trapezoidal intuitionistic fuzzy numbers and its applications to multicriteria decision making","volume":"30","author":"Nayagam","year":"2018","journal-title":"Neural Comput. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10462-025-11200-2","article-title":"Dombi weighted geometric aggregation operators on the class of trapezoidal-valued intuitionistic fuzzy numbers and their applications to multi-attribute group decision-making","volume":"58","author":"Meher","year":"2025","journal-title":"Artif. Intell. Rev."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bihari, R., Jeevaraj, S., and Kumar, A. (2023). A new ranking principle for ordering generalized trapezoidal fuzzy numbers based on diagonal distance, mean and its applications to supplier selection. Soft Comput.","DOI":"10.1007\/s00500-023-08749-x"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"391","DOI":"10.15388\/Informatica.2019.211","article-title":"Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making","volume":"30","author":"Senapati","year":"2019","journal-title":"Informatica"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1007\/s40747-021-00407-9","article-title":"Multi-criteria healthcare waste disposal location selection based on Fermatean fuzzy WASPAS method","volume":"7","author":"Mishra","year":"2021","journal-title":"Complex Intell. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7279027","DOI":"10.1155\/2020\/7279027","article-title":"Decision-making analysis based on Fermatean fuzzy Yager aggregation operators with application in COVID-19 testing facility","volume":"2020","author":"Garg","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"282","DOI":"10.2991\/ijcis.d.201215.001","article-title":"Differential calculus of Fermatean fuzzy functions: Continuities, derivatives, and differentials","volume":"14","author":"Yang","year":"2021","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sergi, D., and Sari, I.U. (2020, January 21\u201323). Fuzzy capital budgeting using Fermatean fuzzy sets. Proceedings of the International Conference on Intelligent and Fuzzy Systems, Istanbul, Turkey.","DOI":"10.1007\/978-3-030-51156-2_52"},{"key":"ref_29","first-page":"18","article-title":"Some score functions on Fermatean fuzzy sets and its application to bride selection based on TOPSIS method","volume":"10","author":"Sahoo","year":"2021","journal-title":"Int. J. Fuzzy Syst. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wu, L., Wei, G., Gao, H., and Wei, Y. (2018). Some interval-valued intuitionistic fuzzy Dombi Hamy mean operators and their application for evaluating the elderly tourism service quality in tourism destination. Mathematics, 6.","DOI":"10.3390\/math6120294"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"128262","DOI":"10.1016\/j.eswa.2025.128262","article-title":"Pure rational and non-pure rational decision methods on interval-valued fuzzy soft \u03b2-covering approximation spaces","volume":"288","author":"Lu","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_32","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra","year":"2010","journal-title":"Int. J. Intell. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"122212","DOI":"10.1016\/j.ins.2025.122212","article-title":"Foundational theories of hesitant fuzzy sets and hesitant fuzzy information systems and their applications for multi-strength intelligent classifiers","volume":"714","author":"Lu","year":"2025","journal-title":"Inf. Sci."},{"key":"ref_34","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":"2022","journal-title":"Int. J. Intell. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Senapati, T., Mesiar, R., Simic, V., Iampan, A., Chinram, R., and Ali, R. (2022). Analysis of interval-valued intuitionistic fuzzy Aczel\u2013Alsina geometric aggregation operators and their application to multiple attribute decision-making. Axioms, 11.","DOI":"10.3390\/axioms11060258"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/7\/1114\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:08:01Z","timestamp":1760033281000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/7\/1114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,10]]},"references-count":35,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["sym17071114"],"URL":"https:\/\/doi.org\/10.3390\/sym17071114","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,7,10]]}}}