Enhancing Web Security Through Complex Cubic q-Rung Orthopair Fuzzy Information

Authors

DOI:

https://doi.org/10.31181/sor31202641

Keywords:

Web services, Complex cubic q-rung orthopair fuzzy set, Complex cubic q-rung orthopair fuzzy relations

Abstract

Over the past two decades, the evolution of web services has profoundly transformed communication and information technologies. As computer programs that facilitate data exchange and interoperability between applications via the Internet, web services play a pivotal role in enabling seamless interactions and information access. However, despite their advantages, these platforms also introduce significant security risks. This study leverages the novel framework of Complex Cubic q-Rung Orthopair Fuzzy Sets (CCuqROFS) to model and address these security threats effectively. Unlike conventional models, CCuqROFS provides a robust structure that incorporates membership (M) and non-membership (NM) degrees, offering a more precise representation of uncertainty. Through illustrative examples, we introduce key concepts such as Complex Cubic q-Rung Orthopair Fuzzy Relations (CCuqROFR), the Cartesian product of CCuqROFSs, and various forms of CCuqROFRs. For the first time in fuzzy set theory, this work systematically examines the relationships between different security threats and countermeasures in web services. The proposed methodologies demonstrate how robust security measures can mitigate the impact of these threats. Finally, a comparative analysis underscores the advantages of our strategies, providing valuable insights for enhancing web service security. 

Downloads

Download data is not yet available.

References

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

Klir, G. J., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: Theory and applications. Prentice Hall.

Dubois, D., & Prade, H. (1980). Fuzzy sets and systems: Theory and applications. Academic Press.

Buckley, J. J. (2006). Fuzzy probability and statistics. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-33190-5

Zimmermann, H. J. (2001). Fuzzy set theory—and its applications (4th ed.). Springer Science & Business Media. https://doi.org/10.1007/978-94-010-0646-0

Jun, Y. B., Kim, C. S., & Yang, K. O. (2012). Cubic sets. Annals of Fuzzy Mathematics and Informatics, 4(1), 83-98.

Mahmood, T., Mehmood, F., & Khan, Q. (2016). Cubic hesitant fuzzy sets and their applications to multi criteria decision making. International Journal of Algebra and Statistics, 5(1), 19-51. https://doi.org/10.20454/ijas.2016.1055

Ramot, D., Milo, R., Friedman, M., & Kandel, A. (2002). Complex fuzzy sets. IEEE Transactions on Fuzzy Systems, 10(2), 171-186. https://doi.org/10.1109/91.995119

Wang, C., Tan, Y., Li, Z., & Agarwal, R. P. (2023). Discrete fuzzy complex-valued function and complex fuzzy Caputo fractional difference equations. Fuzzy Sets and Systems, 465, 108566. https://doi.org/10.1016/j.fss.2023.108566

Tamir, D. E., Rishe, N. D., & Kandel, A. (2015). Complex fuzzy sets and complex fuzzy logic an overview of theory and applications. Fifty years of fuzzy logic and its applications, 661-681. https://doi.org/10.1007/978-3-319-19683-1_31

Wang, X., & Zhang, W. (2007). Complex fuzzy sets and their operations. Journal of Computational Information Systems, 3(1), 197-203.

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3

Dixit, A., & Jain, S. (2023). Intuitionistic fuzzy time series forecasting method for non-stationary time series data with suitable number of clusters and different window size for fuzzy rule generation. Information Sciences, 623, 132-145. https://doi.org/10.1016/j.ins.2022.12.015

Szmidt, E., & Kacprzyk, J. (2010). Correlation of intuitionistic fuzzy sets. In International conference on information processing and management of uncertainty in knowledge-based systems (pp. 169-177). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_18

Szmidt, E., & Kacprzyk, J. (2009). Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In Recent advances in decision making (pp. 7-19). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-02187-9_2

Alkouri, A. M. D. J. S., & Salleh, A. R. (2012). Complex intuitionistic fuzzy sets. In AIP conference proceedings (Vol. 1482, No. 1, pp. 464-470). American Institute of Physics. https://doi.org/10.1063/1.4757515

Garg, H., & Kumar, K. (2019). Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making. Granular Computing, 4(2), 237-247. https://doi.org/10.1007/s41066-018-0092-7

Zimmermann, H. J. (1987). Fuzzy sets in pattern recognition. In Pattern recognition theory and applications (pp. 383-391). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-83069-3_30

Garg, H., & Rani, D. (2019). Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arabian Journal for Science and Engineering, 44(3), 2679-2698. https://doi.org/10.1007/s13369-018-3413-x

Alkouri, A. M. D. J. S., & Salleh, A. R. (2012). Complex intuitionistic fuzzy sets. AIP Conference Proceedings, 1482(1), 464-470. https://doi.org/10.1063/1.4757515

Jan, N., Nasir, A., Alhilal, M. S., Khan, S. U., Pamucar, D., & Alothaim, A. (2021). Investigation of cyber-security and cybercrimes in oil and gas sectors using the innovative structures of complex intuitionistic fuzzy relations. Entropy, 23(9), 1112. https://doi.org/10.3390/e23091112

Garg, H., & Rani, D. (2019). Complex interval-valued intuitionistic fuzzy sets and their aggregation operators. Fundamenta Informaticae, 164(1), 61-101. https://doi.org/10.3233/FI-2019-1755

Nasir, A., Jan, N., Gumaei, A., Khan, S. U., & Albogamy, F. R. (2021). Cybersecurity against the loopholes in industrial control systems using interval-valued complex intuitionistic fuzzy relations. Applied Sciences, 11(16), 7668. https://doi.org/10.3390/app11167668

Garg, H., & Kaur, G. (2019). Cubic Intuitionistic Fuzzy Sets and its Fundamental Properties. Journal of Multiple-Valued Logic & Soft Computing, 33(6). https://api.semanticscholar.org/CorpusID:210118157

Chinnadurai, V., Thayalan, S., & Bobin, A. (2021, May). Multi-criteria decision making process using complex cubic interval valued intuitionistic fuzzy set. In Journal of Physics: Conference Series (Vol. 1850, No. 1, p. 012094). IOP Publishing. https://doi.org/10.1088/1742-6596/1850/1/012094

Mehmood, F., & Liu, H. (2024). Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process. Computing Open, 2, 2450008. https://doi.org/10.1142/S2972370124500089

Garg, H. (2021). Pythagorean Fuzzy Sets. Springer Singapore. https://doi.org/10.1007/978-981-16-1989-2

Wang, W., & Feng, Y. (2023). Pythagorean fuzzy multi-attribute decision making approach with incomplete weight information. Procedia Computer Science, 221, 245-252. https://doi.org/10.1016/j.procs.2023.07.034

Abdullah, L., & Goh, P. (2019). Decision making method based on Pythagorean fuzzy sets and its application to solid waste management. Complex & intelligent systems, 5(2), 185-198. https://doi.org/10.1007/s40747-019-0100-9

Muhammad, S., Ali, R., Abdullah, S., & Okyere, S. (2022). A New Approach to Decision‐Making Problem under Complex Pythagorean Fuzzy Information. Complexity, 2022(1), 8635521. https://doi.org/10.1155/2022/8635521

Yager, R. R. (2015). Properties and applications of Pythagorean fuzzy sets. In Imprecision and Uncertainty in information representation and processing: new tools based on intuitionistic fuzzy sets and generalized nets (pp. 119-136). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-26302-1_9

Ahmed, W., & Mustafa, G. (2025). Complex Pythagorean parameterized fuzzy sets and their applications to countering digital crime and digital terrorism and supply chain management problem. Expert Systems with Applications, 273, 126777. https://doi.org/10.1016/j.eswa.2025.126777

Ejegwa, P. A. (2020). Improved composite relation for Pythagorean fuzzy sets and its application to medical diagnosis. Granular Computing, 5(2), 277-286. https://doi.org/10.1007/s41066-019-00156-8

Ma, X., Akram, M., Zahid, K., & Alcantud, J. C. R. (2021). Group decision-making framework using complex Pythagorean fuzzy information. Neural Computing and Applications, 33(6), 2085-2105. https://doi.org/10.1007/s00521-020-05100-5

Abbas, S. Z., Ali Khan, M. S., Abdullah, S., Sun, H., & Hussain, F. (2019). Cubic Pythagorean fuzzy sets and their application to multi-attribute decision making with unknown weight information. Journal of Intelligent & Fuzzy Systems, 37(1), 1529-1544. https://doi.org/10.3233/JIFS-18382

Akram, M., & Naz, S. (2019). A novel decision-making approach under complex Pythagorean fuzzy environment. Mathematical and Computational Applications, 24(3), 73. https://doi.org/10.3390/mca24030073

Saeed, M., Saeed, M. H., Shafaqat, R., Sessa, S., Ishtiaq, U., & Di Martino, F. (2022). A theoretical development of cubic pythagorean fuzzy soft set with its application in multi-attribute decision making. Symmetry, 14(12), 2639. https://doi.org/10.3390/sym14122639

Khan, F., Khan, M. S. A., Shahzad, M., & Abdullah, S. (2019). Pythagorean cubic fuzzy aggregation operators and their application to multi-criteria decision making problems. Journal of Intelligent & Fuzzy Systems, 36(1), 595-607. https://doi.org/10.3233/JIFS-18943

Ali, M. I. (2018). Another view on q‐rung orthopair fuzzy sets. International Journal of Intelligent Systems, 33(11), 2139-2153. https://doi.org/10.1002/int.22007

Akram, M., Alsulami, S., Karaaslan, F., & Khan, A. (2021). q-Rung orthopair fuzzy graphs under Hamacher operators. Journal of Intelligent & Fuzzy Systems, 40(1), 1367-1390. https://doi.org/10.3233/JIFS-201700

Garg, H. (2022). q-Rung Orthopair Fuzzy Sets. New York, NY, USA: Springer. https://doi.org/10.1007/978-981-19-1449-2

Naz, S., Saeed, M. R., & Butt, S. A. (2024). Multi-attribute group decision-making based on 2-tuple linguistic cubic q-rung orthopair fuzzy DEMATEL analysis. Granular Computing, 9(1), 12. https://doi.org/10.1007/s41066-023-00433-7

Wang, Y., Hussain, A., Mahmood, T., Ali, M. I., Wu, H., & Jin, Y. (2020). Decision‐Making Based on q‐Rung Orthopair Fuzzy Soft Rough Sets. Mathematical Problems in Engineering, 2020(1), 6671001. https://doi.org/10.1155/2020/6671001

Chu, Y. M., Garg, H., Rahim, M., Amin, F., Asiri, A., & Ameer, E. (2024). Some p, q-cubic quasi-rung orthopair fuzzy operators for multi-attribute decision-making. Complex & Intelligent Systems, 10(1), 87-110. https://doi.org/10.1007/s40747-023-01092-6

Wang, J., Shang, X., Bai, K., & Xu, Y. (2020). A new approach to cubic q-rung orthopair fuzzy multiple attribute group decision-making based on power Muirhead mean. Neural Computing and Applications, 32(17), 14087-14112. https://doi.org/10.1007/s00521-020-04807-9

Zhang, B., Mahmood, T., Ahmmad, J., Khan, Q., Ali, Z., & Zeng, S. (2020). Cubic q-Rung orthopair fuzzy Heronian mean operators and their applications to multi-attribute group decision making. Mathematics, 8(7), 1125. https://doi.org/10.3390/math8071125

Ali, Z. (2025). Fairly Aggregation Operators Based on Complex p, q-Rung Orthopair Fuzzy Sets and Their Application in Decision-Making Problems. Spectrum of Operational Research, 2(1), 135-153. https://doi.org/10.31181/sor21202514

Published

2026-01-01

How to Cite

Hussain, S. (2026). Enhancing Web Security Through Complex Cubic q-Rung Orthopair Fuzzy Information. Spectrum of Operational Research, 3(1), 153-182. https://doi.org/10.31181/sor31202641