Exploring Interval-Valued Fermatean Neutrosophic Tactics for Empowering AI-Driven Financial Risk Frameworks: Compliance Automation, Fraud Detection, and Beyond
DOI:
https://doi.org/10.59247/jfsc.v4i1.357Keywords:
Financial Risk Evaluation, Logical Fuzzy Operato, Interval-Valued Fermatean Neutrosophic Numbers (I-VFNNs), Multi-Criteria Decision-Making, Artificial intelligenceAbstract
The financial risk evaluation process, which includes the investigation of the risks related to loans, funding, and trading activities in economic decisions, is greatly utilized in advanced financial systems. However, nowadays in an inconsistent, fast, and digitalized world, conventional risk models are inadequate, particularly when there is ambiguity, inconsistency, or incomplete information provided in the data. In such scenarios, the interference of Artificial Intelligence (AI) is playing a crucial role. Not only are the large data sets dealt with by AI, but also the decision-making processes can be enhanced. Conventional mathematical tools cannot analyze the discipline whose limits are complex, ambiguous, and indeterminate. In this research article, to recognize and analyze these mathematical disciplines, Interval-Valued Fermatean Neutrosophic Numbers (I-VFNNs) are used, an argumentation of modern fuzzy logic. I-VFNNs are particularly mapped out for such circumstances where the information in the data contains uncertainty, ambiguity, or inconsistency. We have used Interval-Valued Fermatean Neutrosophic Numbers (I-VFNNs), an extension of modern fuzzy logic, to identify and analyze these mathematical constraints. In this article, firstly, a list of essential aspects is composed that are affected by Artificial Intelligence in financial risk models, like fraud detection and prevention, stress testing and scenario simulation, automation of regulatory compliance, behavioral risk analysis, enhanced predictive accuracy, dynamic risk modeling, and real-time risk monitoring, etc. All these components we visualized as mathematical disciplines, which are non-probabilistic, irregular, and multifaceted in nature. With the help of I-VFNNs, we portrayed these disciplines in the guise of numbers and demonstrated their influence, intensity, and indeterminacy in accordance with the impact of Artificial intelligence. The results demonstrate that I-VFNNs not only composed ambiguity superiorly, but also refined the disparity between various risk factors. In general, not only are modern ways to constructively assess financial risk models based on Artificial Intelligence (AI) developed, but new approaches in the inspection of indeterminate data using I-VFNNs are furnished in this study. By virtue of this model, in financial organizations, better decisions can be made, accelerate the recognition of risks, and put down the right consideration even in uncertain conditions. In the future, this model can also contribute to other innovative research areas such as international financial policies, large investments, and insurance institutions.
References
M. Fahrezi, “A Systematic Literature Review: The Use of Artificial Intelligence and Machine Learning in Financial Risk Management and Predictive Analytics,” International Journal of Research and Applied Technology, vol. 4, no. 1, pp. 211–223, 2024, https://ojs.unikom.ac.id/index.php/injuratech/article/view/16822.
C. Oko-Odion, “AI-Driven Risk Assessment Models for Financial Markets: Enhancing Predictive Accuracy and Fraud Detection,” International Journal of Computer Applications Technology and Research, vol. 14, pp. 80–96, 2025, https://doi.org/10.7753/ijcatr1404.1007.
D. Aikman et al., “Taking uncertainty seriously: Simplicity versus complexity in financial regulation,” Industrial and Corporate Change, vol. 30, no. 2, pp. 317–345, 2021, https://doi.org/10.1093/icc/dtaa024.
Y. Sari and A. Indrabudiman, “The Role of Artificial Intelligence (AI) in Financial Risk Management,” Formosa Journal of Sustainable Research, vol. 3, no. 9, pp. 2073–2082, 2024, https://doi.org/10.55927/fjsr.v3i9.11436.
L. D. Oyeniyi, C. E. Ugochukwu, and N. Z. Mhlongo, “Transforming financial planning with AI-driven analysis: a review and application insights,” Finance & Accounting Research Journal, vol. 6, no. 4, pp. 626–647, 2024, https://doi.org/10.51594/farj.v6i4.1037.
S. Broumi, R. Sundareswaran, M. Shanmugapriya, P. K. Singh, M. Voskoglou, and M. Talea, “Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets,” Mathematics, vol. 11, no. 18, pp. 3817–3821, 2023, https://doi.org/10.3390/math11183817.
L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965, https://doi.org/10.1016/S0019-9958(65)90241-X.
P. Chotikunnan, W. Khotakham, P. Imura, R. Chotikunnan, A. Wongkamhang, and N. Thongpance, “Comparative Analysis of PID-Driven Data-Based and PSO-Tuned Fuzzy Membership Functions for Robotic Manipulator Control,” Journal of Fuzzy Systems and Control, vol. 3, no. 3, pp. 204–211, 2025, https://doi.org/10.59247/jfsc.v3i3.335.
K. Bhalla, D. Koundal, B. Sharma, Y. C. Hu, and A. Zaguia, “A fuzzy convolutional neural network for enhancing multi-focus image fusion,” Journal of Visual Communication and Image Representation, vol. 84, p. 103485, 2022, https://doi.org/10.1016/j.jvcir.2022.103485.
N. X. Chiem and N. C. B. Nguyen, “Design of Embedded Control System with Fuzzy Controller and Nonlinear Controller for the Line Follower Robot,” Journal of Fuzzy Systems and Control, vol. 3, no. 2, pp. 122–127, 2025, https://doi.org/10.59247/jfsc.v3i2.303.
M. Kamran et al., “A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges,” Symmetry, vol. 16, no. 5, p. 615, 2024, https://doi.org/10.3390/sym16050615.
F. A. Azeez and B. J. Hamza, “Optimizing Hybrid LiFi Communication Systems Using Fuzzy Reinforcement Learning for Enhanced Network Performance,” Journal of Fuzzy Systems and Control, vol. 3, no. 2, pp. 170–173, 2025, https://doi.org/10.59247/jfsc.v3i2.316.
D. K. Sudhish, L. R. Nair, and S. S, “Content-based image retrieval for medical diagnosis using fuzzy clustering and deep learning,” Biomedical Signal Processing and Control, vol. 88, p. 105620, 2024, https://doi.org/10.1016/j.bspc.2023.105620.
H.-T. Nguyen et al., “Experiment Ball Levitation with Fuzzy PID and PID Implementation,” Journal of Fuzzy Systems and Control, vol. 2, no. 3, pp. 129–134, 2024, https://doi.org/10.59247/jfsc.v2i3.221.
J. Więckowski, B. Kizielewicz, A. Shekhovtsov, and W. Sałabun, “How Do the Criteria Affect Sustainable Supplier Evaluation?-A Case Study Using Multi-Criteria Decision Analysis Methods in a Fuzzy Environment,” Journal of Engineering Management and Systems Engineering, vol. 2, no. 1, pp. 37–52, 2023, https://doi.org/10.56578/jemse020102.
A. Uzair, A. Ishtiaq, and M. Rasheed, “Non-kekulean benzenoid hydrocarbon: physico-chemical properties for benzenoid hydrocarbon using topological indices and m-polynomial,” Computational Algorithms and Numerical Dimensions, vol. 3, pp. 94–114, 2024, https://doi.org/10.22105/cand.2024.470538.1100.
S. H. Omran, S. W. Shneen, M. H. Ali, Q. A. Jawad, S. A. Gitaffa, and H. M. Salman, “Comparative Traditional Methods of Attributes with Fuzzy Quality Control Charts for Improving the Quality of a Product,” Journal of Fuzzy Systems and Control, vol. 3, no. 1, pp. 22–29, 2024, https://doi.org/10.59247/jfsc.v3i1.273.
K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986, https://doi.org/10.1016/S0165-0114(86)80034-3.
B. Gohain, R. Chutia, and P. Dutta, “Distance measure on intuitionistic fuzzy sets and its application in decision-making, pattern recognition, and clustering problems,” International Journal of Intelligent Systems, vol. 37, no. 3, pp. 2458–2501, 2022, https://doi.org/10.1002/int.22780.
A. Ishtiaq, K. Tul Kubra, A. Uzair, and A. Ali, “Quantifying Multi-Cause Psychological Disorder Risk Through an Advanced Mathematical Model Using Intuitionistic Pentagonal Fuzzy Logic,” Spectrum of Operational Research, pp. 1–21, 2025, https://doi.org/10.31181/sor41202762.
X. Peng and Y. Yang, “Some Results for Pythagorean Fuzzy Sets,” International Journal of Intelligent Systems, vol. 30, no. 11, pp. 1133–1160, 2015, https://doi.org/10.1002/int.21738.
A. Kumar Adak, D. Kumar, and S. A. Edalatpanah, “Some New Operations on Pythagorean Fuzzy Sets,” Uncertainty Discourse and Applications, vol. 1, no. 1 SE-Articles, pp. 11–19, 2024, https://doi.org/10.48313/uda.v1i1.17.
M. Akram, G. Muhammad, and D. Ahmad, “Analytical solution of the Atangana–Baleanu–Caputo fractional differential equations using Pythagorean fuzzy sets,” Granular Computing, vol. 8, no. 4, pp. 667–687, 2023, https://doi.org/10.1007/s41066-023-00364-3.
T. Senapati and R. R. Yager, “Fermatean fuzzy sets,” Journal of Ambient Intelligence and Humanized Computing, vol. 11, no. 2, pp. 663–674, 2020, https://doi.org/10.1007/s12652-019-01377-0.
J. Chakraborty, S. Mukherjee, and L. Sahoo, “An Alternative Approach for Enhanced Decision-Making using Fermatean Fuzzy Sets,” Spectrum of Engineering and Management Sciences, vol. 2, no. 1, pp. 135–150, 2024, https://doi.org/10.31181/sems21202411j.
M. Kirişci, “New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach,” Knowledge and Information Systems, vol. 65, no. 2, pp. 855–868, 2023, https://doi.org/10.1007/s10115-022-01776-4.
F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics (fourth edition). Rehoboth, NM, USA: American Research Press, 2001. http://arxiv.org/abs/math/0101228.
M. Akram, G. Ali, J. C. R. Alcantud, and A. Riaz, “Group decision-making with Fermatean fuzzy soft expert knowledge,” Artificial Intelligence Review, vol. 55, no. 7, pp. 5349–5389, 2022, https://doi.org/10.1007/s10462-021-10119-8.
C. Delcea, A. Domenteanu, C. Ioanăș, V. M. Vargas, and A. N. Ciucu-Durnoi, “Quantifying Neutrosophic Research: A Bibliometric Study,” Axioms, vol. 12, no. 12, p. 1083, 2023, https://doi.org/10.3390/axioms12121083.
S. Broumi, R. Sundareswaran, M. Shanmugapriya, A. Bakali, and M. Talea, “Theory and Applications of Fermatean Neutrosophic Graphs,” Neutrosophic Sets and Systems, vol. 50, p. 2022, 2022, https://digitalrepository.unm.edu/nss_journal/vol50/iss1/15/.
M. Saeed, M. U. Nisa, M. H. Saeed, T. Alballa, and H. A. E. W. Khalifa, “Detecting Patterns of Infection-Induced Fertility Using Fermatean Neutrosophic Set With Similarity Analysis,” IEEE Access, vol. 11, pp. 112320–112333, 2023, https://doi.org/10.1109/ACCESS.2023.3323024.
N. Gonul Bilgin, D. Pamučar, and M. Riaz, “Fermatean Neutrosophic Topological Spaces and an Application of Neutrosophic Kano Method,” Symmetry, vol. 14, no. 11, 2022, https://doi.org/10.3390/sym14112442.
S. Dhouib, K. Vidhya, S. Broumi, and M. Talea, “Solving the Minimum Spanning Tree Problem Under Interval-Valued Fermatean Neutrosophic Domain,” Neutrosophic Sets and Systems, vol. 67, pp. 11–20, 2024, https://doi.org/10.5281/zenodo.11098903.
M. Kamran, M. Nadeem, J. Żywiołek, M. E. M. Abdalla, A. Uzair, and A. Ishtiaq, “Enhancing Transportation Efficiency with Interval-Valued Fermatean Neutrosophic Numbers: A Multi-Item Optimization Approach,” Symmetry, vol. 16, no. 6, 2024, https://doi.org/10.3390/sym16060766.
Y. Cai, “Interval Valued Fermatean Neutrosophic for Analysis Risk Management of Practical Teaching Quality in University Art and Design Programs,” Neutrosophic Sets and Systems, vol. 83, pp. 27–49, 2025, https://doi.org/10.5281/zenodo.15122386.
M. E. M. Abdalla, A. Uzair, A. Ishtiaq, M. Tahir, and M. Kamran, “Algebraic Structures and Practical Implications of Interval-Valued Fermatean Neutrosophic Super HyperSoft Sets in Healthcare,” Spectrum of Operational Research, vol. 2, no. 1, pp. 240–259, 2025, https://doi.org/10.31181/sor21202523.
M. Saranya and D. Jayanthi, “Novel Cosine Similarity Measures for Interval-Valued Fermatean Neutrosophic Sets with TOPSIS-Based MCDM Applications,” Neutrosophic Sets and Systems, vol. 93, pp. 44–65, 2025, https://doi.org/https://doi.org/10.5281/zenodo.16903431.
B. Ashtiani, F. Haghighirad, A. Makui, and G. A. Montazer, “Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets,” Applied Soft Computing Journal, vol. 9, no. 2, pp. 457–461, Mar. 2009, https://doi.org/10.1016/j.asoc.2008.05.005.
M. G. Paredes-Morales, G. J. Alberdy-Rodriguez, S. G. Morales-Cobos, D. A. Castro-Valderrama, G. A. Valderrama-Barragán, and E. F. Valderrama-Barragán, “A Neutrosophic Model for Assessing the Impact of Artificial Intelligence on Civil Liability,” Neutrosophic Sets and Systems, vol. 81, pp. 382–388, 2025, https://digitalrepository.unm.edu/nss_journal/vol81/iss1/23/.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Aiman Ishtiaq, Khadija Tul Kubra, Anns Uzair, Muhammad Talha Azhar

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.