{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:19:50Z","timestamp":1760149190484,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,13]],"date-time":"2023-07-13T00:00:00Z","timestamp":1689206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University","award":["3775"],"award-info":[{"award-number":["3775"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Airports located in densely populated areas often face challenges due to asymmetrical traffic patterns. Efficient management and careful planning are required to handle the disproportionate flow of passengers, aircraft, and ground services. The significance of symmetry and asymmetry in civil aviation extends to international regulations and agreements. By harmonizing standards and practices among different nations, it is possible to achieve symmetry in safety measures and operational procedures, thereby promoting a unified and secure global aviation system. Conversely, asymmetry in regulations, infrastructure development, or technological advancements among countries can create obstacles in establishing a cohesive and equitable international aviation framework. This article discusses the weaknesses of the existing score function in handling the MADM problem in an Interval-Valued Pythagorean Fuzzy (IVPF) environment. To tackle this issue, an enhanced score function is developed as a solution. The article proposes the IVPF Dombi hybrid arithmetic and IVPF Dombi hybrid geometric operators based on IVPF information. Furthermore, the article proves some fundamental properties of these operators. In the context of recently introduced techniques using IVPF settings, an effective method is developed for selecting the best airline. Additionally, a comparative investigation is carried out to demonstrate the legitimacy and viability of this unique strategy in comparison to earlier approaches.<\/jats:p>","DOI":"10.3390\/sym15071411","type":"journal-article","created":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:28:06Z","timestamp":1689294486000},"page":"1411","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimizing Emergency Plane Selection in Civil Aviation Using Extended Dombi Hybrid Operators"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7579-8972","authenticated-orcid":false,"given":"Asima","family":"Razzaque","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al Ahsa, Al Hofuf 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9146-7145","authenticated-orcid":false,"given":"Ghaliah","family":"Alhamzi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saman","family":"Javaid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umer","family":"Shuaib","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1898-4082","authenticated-orcid":false,"given":"Abdul","family":"Razaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibtisam","family":"Masmali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9038-1921","authenticated-orcid":false,"given":"Saima","family":"Noor","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al Ahsa, Al Hofuf 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,13]]},"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":"141","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_3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0165-0114(78)90010-6","article-title":"Fuzzy decision making including unequal objectives","volume":"1","author":"Yager","year":"1978","journal-title":"Fuzzy Sets Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0165-0114(78)90031-3","article-title":"Fuzzy programming and linear programming with several objective functions","volume":"1","author":"Zimmermann","year":"1978","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","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_6","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_7","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0165-0114(86)90077-1","article-title":"Interval valued fuzzy sets based on normal forms","volume":"20","author":"Turksen","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0165-0114(89)90215-7","article-title":"More on intuitionistic fuzzy sets","volume":"33","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/S0165-0114(98)00191-2","article-title":"Some operations on intuitionistic fuzzy sets","volume":"114","author":"De","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/S0377-2217(99)00082-X","article-title":"On consistency of the weighted geometric mean complex judgement matrix in AHP","volume":"126","author":"Xu","year":"2000","journal-title":"Eur. J. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wei, G., and Wang, X. (2007, January 15\u201319). Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making. Proceedings of the 2007 International Conference on Computational Intelligence and Security (CIS 2007), Harbin, China.","DOI":"10.1109\/CIS.2007.84"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3026","DOI":"10.1016\/j.ins.2009.05.001","article-title":"An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights","volume":"179","author":"Wang","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1080\/03081079.2011.607448","article-title":"Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making","volume":"40","author":"Su","year":"2011","journal-title":"Int. J. Gen. Syst."},{"key":"ref_14","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":"Comput. Ind. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.techfore.2018.12.009","article-title":"Assessment of concentrated solar power (CSP) technologies based on a modified intuitionistic fuzzy topsis and trigonometric entropy weights","volume":"140","author":"Cavallaro","year":"2019","journal-title":"Technol. Forecast. Soc. Change"},{"key":"ref_16","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":"2013","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1109\/TFUZZ.2014.2370675","article-title":"Multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and evidential reasoning methodology","volume":"23","author":"Chen","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2945","DOI":"10.3233\/IFS-130960","article-title":"Induced interval-valued intuitionistic fuzzy Einstein ordered weighted geometric operator and their application to multiple attribute decision making","volume":"26","author":"Yang","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.ins.2017.02.046","article-title":"Multiattribute decision making based on interval-valued intuitionistic fuzzy values and particle swarm optimization techniques","volume":"397","author":"Chen","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.ins.2015.10.012","article-title":"Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods","volume":"330","author":"Zhang","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"529","DOI":"10.3233\/IFS-162165","article-title":"A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem","volume":"31","author":"Garg","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1002\/int.21898","article-title":"A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in the decision-making process","volume":"32","author":"Garg","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1615\/Int.J.UncertaintyQuantification.2017020197","article-title":"A new improved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method","volume":"7","author":"Garg","year":"2017","journal-title":"Int. J. Uncertain. Quantif."},{"key":"ref_25","first-page":"393","article-title":"Some interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operators and their application to group decision making","volume":"29","author":"Rahman","year":"2020","journal-title":"J. Intell. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1338638","DOI":"10.1080\/23311835.2017.1338638","article-title":"Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem","volume":"4","author":"Rahman","year":"2017","journal-title":"Cogent Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1142\/S0218488518500046","article-title":"A linear programming method based on an improved score function for interval-valued Pythagorean fuzzy numbers and its application to decision-making","volume":"26","author":"Garg","year":"2018","journal-title":"Int. J. Uncertain. Fuzziness Knowl.-Based Syst."},{"key":"ref_28","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":"J. Exp. Theor. Artif. Intell."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1615\/Int.J.UncertaintyQuantification.2018020979","article-title":"Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple attribute decision-making","volume":"8","author":"Garg","year":"2018","journal-title":"Int. J. Uncertain. Quantif."},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s41066-018-0091-8","article-title":"Some induced aggregation operators based on interval-valued Pythagorean fuzzy numbers","volume":"4","author":"Rahman","year":"2019","journal-title":"Granul. Comput."},{"key":"ref_32","first-page":"1049","article-title":"New operations for interval-valued Pythagorean fuzzy set","volume":"26","author":"Peng","year":"2019","journal-title":"Sci. Iran."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"7419","DOI":"10.1109\/ACCESS.2018.2890097","article-title":"Algorithms for interval-valued Pythagorean fuzzy sets in emergency decision making based on multiparametric similarity measures and WDBA","volume":"7","author":"Peng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1002\/int.21790","article-title":"Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators","volume":"31","author":"Peng","year":"2016","journal-title":"Int. J. Intell. Syst."},{"key":"ref_35","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_36","doi-asserted-by":"crossref","unstructured":"Wu, L., Wei, G., Wu, J., and Wei, C. (2020). Some interval-valued intuitionistic fuzzy Dombi heronian mean operators and their application for evaluating the ecological value of forest ecological tourism demonstration areas. Int. J. Environ. Res. Public Health, 17.","DOI":"10.3390\/ijerph17030829"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Khan, A.A., Ashraf, S., Abdullah, S., Qiyas, M., Luo, J., and Khan, S.U. (2019). Pythagorean fuzzy Dombi aggregation operators and their application in decision support system. Symmetry, 11.","DOI":"10.3390\/sym11030383"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s40747-018-0076-x","article-title":"Interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator and their application to group decision making","volume":"5","author":"Rahman","year":"2019","journal-title":"Complex Intell. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Alhamzi, G., Javaid, S., Shuaib, U., Razaq, A., Garg, H., and Razzaque, A. (2023). Enhancing Interval-Valued Pythagorean Fuzzy Decision-Making through Dombi-Based Aggregation Operators. Symmetry, 15.","DOI":"10.3390\/sym15030765"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Masmali, I., Hassan, R., Shuaib, U., Razaq, A., Razzaque, A., and Alhamzi, G. (2023). Stock Reordering Decision Making under Interval Valued Picture Fuzzy Knowledge. Symmetry, 15.","DOI":"10.3390\/sym15040898"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Masmali, I., Khalid, A., Shuaib, U., Razaq, A., Garg, H., and Razzaque, A. (2023). On Selection of the Efficient Water Purification Strategy at Commercial Scale Using Complex Intuitionistic Fuzzy Dombi Environment. Water, 15.","DOI":"10.3390\/w15101907"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/7\/1411\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:11:34Z","timestamp":1760127094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/7\/1411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,13]]},"references-count":41,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["sym15071411"],"URL":"https:\/\/doi.org\/10.3390\/sym15071411","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,7,13]]}}}