{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:21:16Z","timestamp":1760710876216,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,26]],"date-time":"2022-01-26T00:00:00Z","timestamp":1643155200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Social Science Fundation of China","award":["15GJ003-227"],"award-info":[{"award-number":["15GJ003-227"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In order to improve the ability of airspace management, a multi-attribute decision-making tool based on q-rung orthopair probability hesitant fuzzy GRA-TOPSIS is proposed to solve the problem of airspace operation effectiveness evaluation; this is in view of the fact that there are few airspace operation effectiveness evaluation methods in general aviation airports. Firstly, taking general aviation airports as the research object, a complete airspace operation effectiveness evaluation system is newly established, its evaluation indicators are introduced, and its multi-attribute decision-making ideas are explained. Then, based on the q-rung orthopair probability hesitant fuzzy set, a new distance measure and information aggregation operator are defined, which can better deal with symmetry information. Secondly, we build a deviation maximization model to calculate the attribute weights of indicator elements in the decision-making process. Then, we combine the GRA method and TOPSIS method to rank the airspace operation effectiveness evaluation schemes. Finally, combined with calculation examples and comparative analysis, the reliability and rationality of the method proposed in this paper are verified, and the symmetry relationship between the evaluation results and the actual situation is better reflected. Experiments show that the method proposed in this paper can obtain more accurate airspace operation effectiveness evaluation results, and can provide reference for related research.<\/jats:p>","DOI":"10.3390\/sym14020242","type":"journal-article","created":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T04:49:51Z","timestamp":1643258991000},"page":"242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Airspace Operation Effectiveness Evaluation Based on q-Rung Orthopair Probabilistic Hesitant Fuzzy GRA and TOPSIS"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9690-982X","authenticated-orcid":false,"given":"Zhiyuan","family":"Chen","sequence":"first","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3534-5311","authenticated-orcid":false,"given":"Di","family":"Shen","sequence":"additional","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"given":"Yaojun","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"given":"Fuping","family":"Yu","sequence":"additional","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"given":"Xiujiu","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Air Force Engineering University, Xi\u2019an 710051, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1109\/TITS.2018.2839344","article-title":"Mathematical Models for Air Traffic Conflict and Collision Probability Estimation","volume":"20","author":"Mitici","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, S., Zhang, H., Li, Z., and Liu, H. (2021). An Air Route Network Planning Model of Logistics UAV Terminal Distribution in Urban Low Altitude Airspace. Sustainability, 13.","DOI":"10.3390\/su132313079"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Moreira, M.\u00c2., de Ara\u00fajo Costa, I.P., Pereira, M.T., dos Santos, M., Gomes, C.F., and Muradas, F.M. (2021). PROMETHEE-SAPEVO-M1 a Hybrid Approach Based on Ordinal and Cardinal Inputs: Multi-Criteria Evaluation of Helicopters to Support Brazilian Navy Operations. Algorithms, 14.","DOI":"10.3390\/a14050140"},{"key":"ref_4","first-page":"1","article-title":"Estimation of Airspace Sector Capacity using A Macroscopic Approach: A Case Study of North Sector in Incheon ACC","volume":"26","author":"Kim","year":"2019","journal-title":"J. Transp. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.trc.2018.07.032","article-title":"Dynamic airspace sectorisation for flight-centric operations","volume":"95","author":"Gerdes","year":"2018","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3233","DOI":"10.1109\/TITS.2019.2924981","article-title":"Tackling Uncertainty for the Development of Efficient Decision Support System in Air Traffic Management","volume":"21","author":"Scala","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5904","DOI":"10.1109\/TITS.2020.3046103","article-title":"Improving Productivity of Low-Altitude Airspace: Speed vs Direction Control","volume":"22","author":"Bulusu","year":"2021","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yang, L., Li, W., Wang, S., and Zhao, Z. (2021). Multi-Attributes Decision-Making for CDO Trajectory Planning in a Novel Terminal Airspace. Sustainability, 13.","DOI":"10.3390\/su13031354"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e20210011","DOI":"10.1590\/0103-6513.20210011","article-title":"Multi-criteria analysis applied to aircraft selection by Brazilian Navy","volume":"31","author":"Costa","year":"2021","journal-title":"Production"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1057\/kmrp.2011.6","article-title":"The success of Expert Recommending Services and the part played by organizational context","volume":"9","author":"Claudio","year":"2011","journal-title":"Knowl. Manag. Res. Pract."},{"key":"ref_11","unstructured":"Justyna, P.M., and Irene, K. (2016, January 13\u201315). A Model of the Tacit Knowledge Transfer Support Tool: CKnow-Board. Proceedings of the International Conference on Information and Software Technologies, Druskininkai, Lithuania."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"6662254","DOI":"10.1155\/2021\/6662254","article-title":"Fuzzy Frequent Pattern Mining Algorithm Based on Weighted Sliding Window and Type-2 Fuzzy Sets over Medical Data Stream","volume":"2021","author":"Chen","year":"2021","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1109\/TFUZZ.2019.2923958","article-title":"A Unified View of Different Axiomatic Measures Defined on $L$-Fuzzy Sets","volume":"28","author":"Couso","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Farhadinia, B., and Chiclana, F. (2021). Extended Fuzzy Sets and Their Applications. Mathematics, 9.","DOI":"10.3390\/math9070770"},{"key":"ref_16","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 Set Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"196075","DOI":"10.1109\/ACCESS.2020.3034626","article-title":"A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory","volume":"8","author":"Gulzar","year":"2020","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1007\/s12559-021-09884-z","article-title":"Commentary on \u201cD-Intuitionistic Hesitant Fuzzy Sets and Their Application in Multiple Attribute Decision Making\u201d","volume":"13","author":"Mishra","year":"2021","journal-title":"Cogn. Comput."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","article-title":"Generalized Orthopair Fuzzy Sets","volume":"25","author":"Yager","year":"2017","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ghoushchi, S.J., Bonab, S.R., Ghiaci, A.M., Haseli, G., Tomaskova, H., and Hajiaghaei-Keshteli, M. (2021). Landfill Site Selection for Medical Waste Using an Integrated SWARA-WASPAS Framework Based on Spherical Fuzzy Set. Sustainability, 13.","DOI":"10.3390\/su132413950"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1974","DOI":"10.1109\/TFUZZ.2019.2893205","article-title":"Integrations of q-Rung Orthopair Fuzzy Continuous Information","volume":"27","author":"Shu","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3220","DOI":"10.1002\/int.22191","article-title":"Some Dombi aggregation of Q-rung orthopair fuzzy numbers in multiple-attribute decision making","volume":"34","author":"Jana","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2151","DOI":"10.1002\/int.22137","article-title":"Additive consistency-based priority-generating method of q-rung orthopair fuzzy preference relation","volume":"34","author":"Zhang","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_25","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"TORRA","year":"2010","journal-title":"Int. J. Intell. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"59774","DOI":"10.1109\/ACCESS.2020.2982892","article-title":"Hesitant Fuzzy Concept Lattice and its Application","volume":"8","author":"Yang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4223","DOI":"10.1007\/s00500-019-04187-w","article-title":"Hesitant fuzzy soft multisets and their applications in decision-making problems","volume":"24","author":"Kandil","year":"2019","journal-title":"Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2104","DOI":"10.1002\/int.22133","article-title":"The distance measures between q-rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making","volume":"34","author":"Liu","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ren, Y.J., Yuan, X.J., and Lin, R.J. (2021). A novel MADM algorithm for landfill site selection based on q-rung orthopair probabilistic hesitant fuzzy power Muirhead mean operator. PLoS ONE, 16.","DOI":"10.21203\/rs.3.rs-701025\/v1"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6652586","DOI":"10.1155\/2021\/6652586","article-title":"Extended TOPSIS Method for Supplier Selection under Picture Hesitant Fuzzy Environment Using Linguistic Variables","volume":"2021","author":"Ambrin","year":"2021","journal-title":"J. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"873","DOI":"10.3233\/JIFS-179455","article-title":"Application of interval valued intuitionistic fuzzy TOPSIS for flood management","volume":"38","author":"Abdullah","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hwang, C.L., and Yoon, K. (1981). Methods for multiple attribute decision making. Multiple Attribute Decision Making, Springer.","DOI":"10.1007\/978-3-642-48318-9"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/03081060.2020.1717147","article-title":"Simplified likelihood estimation of ship total loss using GRA and CRITIC methods","volume":"43","author":"Xu","year":"2020","journal-title":"Transp. Plan. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4721","DOI":"10.3233\/JIFS-191416","article-title":"Probabilistic linguistic GRA method for multiple attribute group decision making","volume":"38","author":"Wei","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_35","first-page":"1","article-title":"Introduction to grey system","volume":"1","author":"Deng","year":"1989","journal-title":"J. Grey Syst."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wang, C.N., Nguyen, N.A., Dang, T.T., and Lu, C.M. (2021). A Compromised Decision-Making Approach to Third-Party Logistics Selection in Sustainable Supply Chain Using Fuzzy AHP and Fuzzy VIKOR Methods. Mathematics, 9.","DOI":"10.3390\/math9080886"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"115594","DOI":"10.1016\/j.eswa.2021.115594","article-title":"Recovery solutions for ecotourism centers during the COVID-19 pandemic: Utilizing Fuzzy DEMATEL and Fuzzy VIKOR methods","volume":"185","author":"Hosseini","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_38","unstructured":"Opricovic, S. (1998). Multi Criteria Optimization of Civil Engineering Systems, Faculty of Civil Engineering."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"103374","DOI":"10.1016\/j.trc.2021.103374","article-title":"A probabilistic model based optimization for aircraft scheduling in terminal area under uncertainty","volume":"132","author":"Huo","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1016\/j.eswa.2014.08.056","article-title":"Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis","volume":"42","author":"Zhang","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"9957505","DOI":"10.1155\/2021\/9957505","article-title":"GRA and CRITIC Method for Intuitionistic Fuzzy Multiattribute Group Decision Making and Application to Development Potentiality Evaluation of Cultural and Creative Garden","volume":"2021","author":"Qi","year":"2021","journal-title":"Math. Probl. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:08:11Z","timestamp":1760134091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,26]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020242"],"URL":"https:\/\/doi.org\/10.3390\/sym14020242","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,1,26]]}}}