{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:34:00Z","timestamp":1762342440992,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T00:00:00Z","timestamp":1733875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12201466","SK2020A0398","2022AH040240","2024AH053477","2023ZD008"],"award-info":[{"award-number":["12201466","SK2020A0398","2022AH040240","2024AH053477","2023ZD008"]}]},{"name":"Humanities and Social Sciences Key Grant Foundation of the Education Department of Anhui Province of China","award":["12201466","SK2020A0398","2022AH040240","2024AH053477","2023ZD008"],"award-info":[{"award-number":["12201466","SK2020A0398","2022AH040240","2024AH053477","2023ZD008"]}]},{"name":"Innovative Development of Social Sciences of Anhui Province of China","award":["12201466","SK2020A0398","2022AH040240","2024AH053477","2023ZD008"],"award-info":[{"award-number":["12201466","SK2020A0398","2022AH040240","2024AH053477","2023ZD008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Linguistic q-Rung orthopair fuzzy set is a new extension of the linguistic Pythagorean fuzzy set, which effectively represents the fuzzy and uncertain decision-making information based on qualitative modeling. However, its operational rules are unable to process pure linguistic exponential calculations, in which the exponents are represented using linguistic q-Rung orthopair fuzzy values and the bases are represented as linguistic terms or interval linguistic numbers. This greatly restricts its application in decision making under complex environments. As the complement of the existing linguistic q-Rung orthopair fuzzy operational rules, this paper defines linguistic q-Rung orthopair fuzzy calculation rules, including division, subtraction, and exponent operations. Based on theorem-based proofs, the relevant properties of the calculation rules have been analyzed, such as commutative law, distributive law, symmetry, and so on. Moreover, in order to facilitate the application of linguistic q-Rung orthopair fuzzy theory, this paper introduces the concept of dual linguistic q-Rung orthopair fuzzy value. Building on this foundation, a series of weighted aggregation operators for the calculations involving linguistic q-Rung orthopair fuzzy values and dual linguistic q-Rung orthopair fuzzy values have been designed. In conclusion, a novel pure linguistic multi criteria decision-making methodology is introduced in this work. The validity and utility of the proposed method are demonstrated via a real-world application in the decision process of energy resource exploitation.<\/jats:p>","DOI":"10.3390\/sym16121641","type":"journal-article","created":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T12:58:49Z","timestamp":1733921929000},"page":"1641","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Novel Approach for Multi-Criteria Decision-Making Problem with Linguistic q-Rung Orthopair Fuzzy Attribute Weight Information"],"prefix":"10.3390","volume":"16","author":[{"given":"Minghua","family":"Shi","sequence":"first","affiliation":[{"name":"College of Finance and Mathematics, West Anhui University, Lu\u2019an 237012, China"},{"name":"Anhui Provincial Key Laboratory of Philosophy and Social Sciences for Data Intelligence and Rural Revitalization of Dabie Mountains, Lu\u2019an 237012, China"}]},{"given":"Jinbo","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Finance and Mathematics, West Anhui University, Lu\u2019an 237012, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,11]]},"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":"57","DOI":"10.1007\/s12652-022-03873-2","article-title":"Extension of SIR method with interval type 2-hesitant fuzzy set to aggrandize industry-university collaboration projects in South Korea","volume":"15","author":"Selvaraj","year":"2024","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_3","first-page":"030029","article-title":"Some operations on circular intuitionistic fuzzy sets","volume":"2905","author":"Dian","year":"2024","journal-title":"AIP Conf. Proc."},{"key":"ref_4","first-page":"423","article-title":"Approach to Multiple Attribute Group Decision Making Based on Hesitant Fuzzy Linguistic Aggregation Operators","volume":"29","author":"Shi","year":"2020","journal-title":"J. Intell. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3367","DOI":"10.1109\/TFUZZ.2019.2950881","article-title":"Limit Theory and Differential Calculus of Intuitionistic Fuzzy Functions with Several Variables","volume":"28","author":"Ai","year":"2020","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.matcom.2023.12.021","article-title":"Distance and similarity measures of Hesitant bi-fuzzy set and its applications in renewable energy systems","volume":"219","author":"Gupta","year":"2024","journal-title":"Math. Comput. Simul."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"111427","DOI":"10.1016\/j.asoc.2024.111427","article-title":"TSFIS-GWO: Metaheuristic-driven takagi-sugeno fuzzy system for adaptive real-time routing in WBANs","volume":"155","author":"Memarian","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107401","DOI":"10.1016\/j.asoc.2021.107401","article-title":"FH-ACO: Fuzzy heuristic-based ant colony optimization for joint virtual network function placement and routing","volume":"107","author":"Shokouhifar","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"120729","DOI":"10.1016\/j.eswa.2023.120729","article-title":"PRV-FCM: An extension of fuzzy cognitive maps for prescriptive modeling","volume":"231","author":"Hoyos","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"B141","DOI":"10.1287\/mnsc.17.4.B141","article-title":"Decision-Making in a Fuzzy Environment","volume":"17","author":"Bellman","year":"1970","journal-title":"Manag. Sci."},{"key":"ref_11","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_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":"3853","DOI":"10.1007\/s40747-023-01329-4","article-title":"Hamacher interaction aggregation operators for complex intuitionistic fuzzy sets and their applications in green supply chain management","volume":"10","author":"Liu","year":"2024","journal-title":"Complex Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2458","DOI":"10.1002\/int.22780","article-title":"Distance measure on intuitionistic fuzzy sets and its application in decision-making, pattern recognition, and clustering problems","volume":"37","author":"Gohain","year":"2022","journal-title":"Int. J. Intell. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108522","DOI":"10.1016\/j.engappai.2024.108522","article-title":"Similarity measure on intuitionistic fuzzy sets based on Benchmark Line and it\u2019s diverse applications","volume":"133","author":"Dutta","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yager, R.R. (2013, January 24\u201328). Pythagorean fuzzy subsets. Proceedings of the Ifsa World Congress and Nafips Meeting, Edmonton, AB, Canada.","DOI":"10.1109\/IFSA-NAFIPS.2013.6608375"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","article-title":"Pythagorean Membership Grades in Multicriteria Decision Making","volume":"22","author":"Yager","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1002\/int.21676","article-title":"Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets","volume":"29","author":"Zhang","year":"2014","journal-title":"Int. J. Intell. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4373","DOI":"10.1007\/s40747-024-01376-5","article-title":"Group decision on rationalizing disease analysis using novel distance measure on Pythagorean fuzziness","volume":"10","author":"Baranidharan","year":"2024","journal-title":"Complex Intell. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1007\/s40815-022-01404-x","article-title":"Pythagorean Fuzzy Based AHP-VIKOR Integration to Assess Rail Transportation Systems in Turkey","volume":"25","author":"Demir","year":"2023","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s41066-023-00436-4","article-title":"Pythagorean fuzzy information-based MCGDM method for assessing the metaverse incorporated sharing economy applications in the transportation sector","volume":"9","author":"Goyal","year":"2024","journal-title":"Granul. Comput."},{"key":"ref_22","first-page":"1222","article-title":"Generalized orthopair fuzzy sets","volume":"26","author":"Yager","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"31975","DOI":"10.1109\/ACCESS.2021.3059683","article-title":"Some Geometric Aggregation Operators Under q-Rung Orthopair Fuzzy Soft Information with Their Applications in Multi-Criteria Decision Making","volume":"9","author":"Chinram","year":"2021","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.ins.2019.11.035","article-title":"Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets","volume":"517","author":"Garg","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4262","DOI":"10.1109\/TFUZZ.2023.3280221","article-title":"Alcantud.Complemental Fuzzy Sets: A Semantic Justification of q-Rung Orthopair Fuzzy Sets","volume":"31","year":"2023","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1002\/int.21979","article-title":"Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process","volume":"33","author":"Garg","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/int.22136","article-title":"Linguistic q-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators","volume":"35","author":"Lin","year":"2020","journal-title":"Int. J. Intell. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4111","DOI":"10.3233\/JIFS-200244","article-title":"The reference ideal TOPSIS method for linguistic q-rung orthopair fuzzy decision making based on linguistic scale function","volume":"39","author":"Liu","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_29","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","author":"Akram","year":"2021","journal-title":"Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1007\/s41066-023-00404-y","article-title":"Group decision making approach based on linguistic q-rung orthopair fuzzy generalized shapley bi-direction Choquet-copula operators","volume":"8","author":"Wang","year":"2023","journal-title":"Granul. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s41066-024-00478-2","article-title":"Multiattribute group decision-making based on weighted correlation coefficient of linguistic q-rung orthopair fuzzy sets and TOPSIS method","volume":"9","author":"Arora","year":"2024","journal-title":"Granul. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"129","DOI":"10.3233\/IFS-151739","article-title":"New operational laws and aggregation method of intuitionistic fuzzy information","volume":"30","author":"Gou","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s13042-015-0434-6","article-title":"Exponential operations of interval-valued intuitionistic fuzzy numbers","volume":"7","author":"Gou","year":"2016","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_34","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":"Int. J. Intell. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1002\/int.22028","article-title":"Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function","volume":"33","author":"Peng","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"13937","DOI":"10.1007\/s00521-021-06036-0","article-title":"New exponential operation laws and operators for interval-valued q-rung orthopair fuzzy sets in group decision making process","volume":"33","author":"Garg","year":"2021","journal-title":"Neural Comput. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Rehman, A.U., Gulistan, M., Ali, M., Al-Shamiri, M.M., and Abdulla, S. (2023). Development of neutrosophic cubic hesitant fuzzy exponential aggregation operators with application in environmental protection problems. Sci. Rep., 13.","DOI":"10.1038\/s41598-022-22399-3"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"41767","DOI":"10.1007\/s11042-023-14532-9","article-title":"Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making","volume":"82","author":"Ajay","year":"2023","journal-title":"Multimed. Tools Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1007\/s41066-023-00448-0","article-title":"Multi-criteria decision-making based on intuitionistic fuzzy exponential knowledge and similarity measure and improved VIKOR method","volume":"9","author":"Kansal","year":"2024","journal-title":"Granul. Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.inffus.2016.06.002","article-title":"On the syntax and semantics of virtual linguistic terms for information fusion in decision making","volume":"34","author":"Xu","year":"2017","journal-title":"Inf. Fusion"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.3233\/IFS-141137","article-title":"Multi-criteria decision making with intuitionistic fuzzy PROMETHEE","volume":"27","author":"Liao","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2651","DOI":"10.3233\/JIFS-182903","article-title":"Intuitionistic fuzzy power geometric Heronian mean operators and their application to multiple attribute decision making","volume":"37","author":"Shi","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1007\/s40815-023-01672-1","article-title":"Group Decision Making Based on Generalized Intuitionistic Fuzzy Yager Weighted Heronian Mean Aggregation Operator","volume":"26","author":"Wang","year":"2024","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"10029","DOI":"10.1007\/s00500-018-3558-2","article-title":"Intuitionistic fuzzy reducible weighted Maclaurin symmetric means and their application in multiple-attribute decision making","volume":"23","author":"Shi","year":"2019","journal-title":"Soft Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1002\/int.22005","article-title":"Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making","volume":"33","author":"Teng","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.asoc.2008.05.005","article-title":"Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets","volume":"9","author":"Ashtiani","year":"2009","journal-title":"Appl. Soft Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1142\/S0218488513500347","article-title":"Some induced uncertain geometric aggregation operators with pure linguistic information and their application to group decision making","volume":"21","author":"Peng","year":"2013","journal-title":"Int. J. Uncertain. Fuzziness Knowl. Based Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1641\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:52:45Z","timestamp":1760115165000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1641"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,11]]},"references-count":47,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["sym16121641"],"URL":"https:\/\/doi.org\/10.3390\/sym16121641","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,12,11]]}}}