{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T02:13:03Z","timestamp":1774663983338,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,19]],"date-time":"2025-01-19T00:00:00Z","timestamp":1737244800000},"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>Financial Risk Management (FRM) is crucial for organizations navigating complex and volatile economic conditions, as it aids in identifying and mitigating potential losses. Conventional FRM approaches are inadequate because they do not incorporate vagueness and variability in financial data. To overcome these challenges, this research presents interval-valued picture fuzzy measurement alternatives and rankings according to the Compromise Solution (IVPF-MARCOS) method. The IVPF-MARCOS method ranks investment strategies under uncertainty by assessing ten distinct investment options across seven key factors, including market risk and return on investment. It evidences its usefulness in enhancing decision-making, increasing accuracy in FRM, and developing Multi-Criteria Group Decision-Making (MCGDM) methodologies involving aggregation operators that are symmetric in nature. Consequently, this research establishes a compelling need to adopt improved fuzzy techniques in formulating the FRM to achieve more robust financial strategies.<\/jats:p>","DOI":"10.3390\/sym17010144","type":"journal-article","created":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T04:04:12Z","timestamp":1737345852000},"page":"144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Robust Large-Scale Multi-Criteria Decision Algorithm for Financial Risk Management with Interval-Valued Picture Fuzzy Information"],"prefix":"10.3390","volume":"17","author":[{"given":"Na","family":"Shang","sequence":"first","affiliation":[{"name":"School of Economics, Minzu University of China, Beijing 712000, China"},{"name":"School of Economics, Wuhai Vocational and Technical College, Wuhai 016000, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1111-8897","authenticated-orcid":false,"given":"Hongfei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics, Minzu University of China, Beijing 712000, China"},{"name":"School of Economics, Hebei University of Engineering, Handan 056038, China"}]},{"given":"Jie","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Economics, Wuhai Vocational and Technical College, Wuhai 016000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Akomea-Frimpong, I., Jin, X., and Osei-Kyei, R. (2024). Fuzzy Analysis of Financial Risk Management Strategies for Sustainable Public\u2013Private Partnership Infrastructure Projects in Ghana. Infrastructures, 9.","DOI":"10.20944\/preprints202403.1112.v2"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2281","DOI":"10.3233\/JIFS-233395","article-title":"An Integrated Methodology for Enterprise Financial Management Capability Evaluation Based on EDAS Technique and Group Decision Making","volume":"46","author":"Mu","year":"2024","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-7908-1870-3_1","article-title":"Intuitionistic Fuzzy Sets","volume":"Volume 35","author":"Atanassov","year":"1999","journal-title":"Intuitionistic Fuzzy Sets"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yager, R.R. (2013, January 24\u201328). Pythagorean Fuzzy Subsets. Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA\/NAFIPS), Edmonton, AB, Canada.","DOI":"10.1109\/IFSA-NAFIPS.2013.6608375"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Cuong, B. (2013). Picture Fuzzy Sets-First Results, Part 1: Seminar Neuro-Fuzzy Systems with Applications.","DOI":"10.1109\/WICT.2013.7113099"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"51236","DOI":"10.1109\/ACCESS.2019.2910844","article-title":"New Operations on Interval-Valued Picture Fuzzy Set, Interval-Valued Picture Fuzzy Soft Set and Their Applications","volume":"7","author":"Khalil","year":"2019","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2014.02.137","article-title":"Evaluation of Clustering Algorithms for Financial Risk Analysis Using MCDM Methods","volume":"275","author":"Kou","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s13748-020-00207-1","article-title":"Ranking-Based MCDM Models in Financial Management Applications: Analysis and Emerging Challenges","volume":"9","year":"2020","journal-title":"Prog. Artif. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Czarnowski, I., Howlett, R.J., and Jain, L.C. (2020). IVIFCM-TOPSIS for Bank Credit Risk Assessment. Intelligent Decision Technologies 2019, Springer.","DOI":"10.1007\/978-981-13-8311-3"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1007\/s40815-022-01401-0","article-title":"VIKOR Method for Plithogenic Probabilistic Linguistic MAGDM and Application to Sustainable Supply Chain Financial Risk Evaluation","volume":"25","author":"Wang","year":"2023","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, W., Wang, L., and Rehman, O.U. (2024). A Novel Interval Type-2 Fuzzy CPT-TODIM Method for Multi-Criteria Group Decision Making and Its Application to Credit Risk Assessment in Supply Chain Finance. International Journal of Fuzzy Systems, Springer.","DOI":"10.1007\/s40815-024-01759-3"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"101851","DOI":"10.1016\/j.seps.2024.101851","article-title":"A Single-Valued Neutrosophic CIMAS-CRITIC-RBNAR Decision Support Model for the Financial Performance Analysis: A Study of Technology Companies","volume":"92","author":"Kara","year":"2024","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"203203","DOI":"10.1109\/ACCESS.2020.3036322","article-title":"Machine Learning for Financial Risk Management: A Survey","volume":"8","author":"Mashrur","year":"2020","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Li, D.-P., Cheng, S.-J., Cheng, P.-F., Wang, J.-Q., and Zhang, H.-Y. (2018). A Novel Financial Risk Assessment Model for Companies Based on Heterogeneous Information and Aggregated Historical Data. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0208166"},{"key":"ref_17","first-page":"21","article-title":"Innovation in Financial Health Assessment: Applying MCDM Techniques to Banks in Vietnam","volume":"12","author":"Trung","year":"2024","journal-title":"Econ. Innov. Econ. Res. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"e31615","DOI":"10.1016\/j.heliyon.2024.e31615","article-title":"Z-Number Based Fuzzy MCDM Models for Analyzing Non-Traditional Security Threats to Finance Supply Chains: A Case Study from Vietnam","volume":"10","author":"Nguyen","year":"2024","journal-title":"Heliyon"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Alsanousi, A.T., Alqahtani, A.Y., Makki, A.A., and Baghdadi, M.A. (2024). A Hybrid MCDM Approach Using the BWM and the TOPSIS for a Financial Performance-Based Evaluation of Saudi Stocks. Information, 15.","DOI":"10.3390\/info15050258"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1108\/CI-01-2021-0008","article-title":"Introducing a Fuzzy MCDM Model for Financial Management in Multiple Project Environments","volume":"22","author":"Afshar","year":"2022","journal-title":"Constr. Innov."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"105892","DOI":"10.1016\/j.engappai.2023.105892","article-title":"An Extended MARCOS Method for MCGDM under 2-Tuple Linguistic q-Rung Picture Fuzzy Environment","volume":"120","author":"Akram","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s10479-023-05453-9","article-title":"An Integrated Pythagorean Fuzzy Fairly Operator-Based MARCOS Method for Solving the Sustainable Circular Supplier Selection Problem","volume":"342","author":"Mishra","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1007\/s40314-022-02080-1","article-title":"Improving Emergency Departments during COVID-19 Pandemic: A Simulation and MCDM Approach with MARCOS Methodology in an Uncertain Environment","volume":"41","author":"Garg","year":"2022","journal-title":"Comp. Appl. Math."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kumar, S., Bhaumik, S., Patnaik, L., Maity, S.R., and Paleu, V. (2022). Application of Integrated BWM Fuzzy-MARCOS Approach for Coating Material Selection in Tooling Industries. Materials, 15.","DOI":"10.3390\/ma15249002"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"313","DOI":"10.31181\/dmame7220241137","article-title":"Measurement of Alternatives and Ranking According to Compromise Solution (MARCOS) Method: A Comprehensive Bibliometric Analysis","volume":"7","author":"Demir","year":"2024","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1016\/j.ijhydene.2024.06.199","article-title":"Evaluation and Selection of Sustainable Hydrogen Production Technologies with Unknown Expert Weights Based on Extended MARCOS under Hybrid Information","volume":"77","author":"Zhan","year":"2024","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s41066-024-00480-8","article-title":"Multicriteria Group Decision Making for Prioritizing IoT Risk Factors with Linear Diophantine Fuzzy Sets and MARCOS Method","volume":"9","author":"Jayakumar","year":"2024","journal-title":"Granul. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"28601","DOI":"10.1016\/j.ijhydene.2023.04.019","article-title":"Performance-Emission Optimization in a Single Cylinder CI-Engine with Diesel Hydrogen Dual Fuel: A Spherical Fuzzy MARCOS MCGDM Based Type-3 Fuzzy Logic Approach","volume":"48","author":"Tarafdar","year":"2023","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Nguyen, T.T.T., Dang, T.-T., and Nguyen, N.-A.-T. (2022). A Hybrid OPA and Fuzzy MARCOS Methodology for Sustainable Supplier Selection with Technology 4.0 Evaluation. Processes, 10.","DOI":"10.3390\/pr10112351"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Garg, H. (2022). MARCOS Technique by Using Q-Rung Orthopair Fuzzy Sets for Evaluating the Performance of Insurance Companies in Terms of Healthcare Services. q-Rung Orthopair Fuzzy Sets, Springer Nature.","DOI":"10.1007\/978-981-19-1449-2"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"119456","DOI":"10.1016\/j.ins.2023.119456","article-title":"Advancing Individual Decision-Making: An Extension of the Characteristic Objects Method Using Expected Solution Point","volume":"647","author":"Shekhovtsov","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_32","unstructured":"Franco, L., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., and Sloot, P.M.A. (2024). SESP-SPOTIS: Advancing Stochastic Approach for Re-Identifying MCDA Models. Computational Science\u2014ICCS 2024, Springer Nature."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"101442","DOI":"10.1016\/j.esr.2024.101442","article-title":"Energy Supplier Selection by TOPSIS Method Based on Multi-Attribute Decision-Making by Using Novel Idea of Complex Fuzzy Rough Information","volume":"54","author":"Hussain","year":"2024","journal-title":"Energy Strategy Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"108689","DOI":"10.1016\/j.asoc.2022.108689","article-title":"An Extended Interval-Valued Pythagorean Fuzzy WASPAS Method Based on New Similarity Measures to Evaluate the Renewable Energy Sources","volume":"120","author":"Mishra","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.ijhydene.2023.10.081","article-title":"Sustainable Stationary Hydrogen Storage Application Selection with Interval-Valued Intuitionistic Fuzzy AHP","volume":"49","author":"Acar","year":"2024","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_36","first-page":"3249","article-title":"Khawla Spearman\u2019s Correlation Coefficient in Statistical Analysis","volume":"13","year":"2022","journal-title":"Int. J. Nonlinear Anal. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"109085","DOI":"10.1016\/j.engappai.2024.109085","article-title":"Intuitionistic Fuzzy Sugeno-Weber Decision Framework for Sustainable Digital Security Assessment","volume":"137","author":"Hussain","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Krzhizhanovskaya, V.V., Z\u00e1vodszky, G., Lees, M.H., Dongarra, J.J., Sloot, P.M.A., Brissos, S., and Teixeira, J. (2020). A New Coefficient of Rankings Similarity in Decision-Making Problems. Computational Science\u2014ICCS 2020, Springer International Publishing.","DOI":"10.1007\/978-3-030-50436-6"},{"key":"ref_39","first-page":"381","article-title":"Towards Reliable Decision-Making in the Green Urban Transport Domain","volume":"20","author":"Shekhovtsov","year":"2022","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"6190936","DOI":"10.1155\/2020\/6190936","article-title":"Adaptive Inventory Control Based on Fuzzy Neural Network under Uncertain Environment","volume":"2020","author":"Ge","year":"2020","journal-title":"Complexity"},{"key":"ref_41","first-page":"1712","article-title":"Fuzzy Fixed Point Results and Applications to Ordinary Fuzzy Differential Equations in Complex Valued Metric Spaces","volume":"48","author":"Sarwar","year":"2019","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_42","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_43","first-page":"127479","article-title":"Sliding Mode Control of Discrete-Time Interval Type-2 Fuzzy Markov Jump Systems with the Preview Target Signal","volume":"435","author":"Sun","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"ref_44","first-page":"127153","article-title":"Observer-Based Sliding Mode Control for Fuzzy Stochastic Switching Systems with Deception Attacks","volume":"427","author":"Zhang","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"ref_45","first-page":"125001","article-title":"SMC for Semi-Markov Jump TS Fuzzy Systems with Time Delay","volume":"374","author":"Gao","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"ref_46","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"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/144\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:31:46Z","timestamp":1759919506000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,19]]},"references-count":46,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["sym17010144"],"URL":"https:\/\/doi.org\/10.3390\/sym17010144","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,19]]}}}