Fairly Aggregation Operators Based on Complex p, q-Rung Orthopair Fuzzy Sets and Their Application in Decision-Making Problems

Authors

DOI:

https://doi.org/10.31181/sor21202514

Keywords:

Decision-making, Complex p, q-Rung orthopair fuzzy sets, Fairly aggregation operators, Fuzzy sets

Abstract

The decision-making technique is used to evaluate the best optimal among the collection of finite alternatives. Further, the technique of complex p, q-rung orthopair fuzzy (CPQROF) set is very reliable and dominant due to parameters “p” and “q”. In contrast, the technique of simple q-rung orthopair fuzzy sets is the special case of the CPQROF set. The major theme of this article is to expose the novel theory of fairly operational laws based on CPQROF numbers (CPQROFNs). Further, we evaluate the weighted fairly aggregation operators based on CPQROF information, called CPQROF weighted fairly averaging (CPQROFWFA) operator and CPQROF ordered weighted fairly averaging (CPQROFOWFA) operator. Some properties are also discussed for the above operators. Additionally, we validate the system of multi-attribute decision-making (MADM) difficulties based on initiated operators. Finally, we associate our suggested ranking consequences with approximately prevailing techniques to demonstrate the proposed theory's sovereignty and validity. 

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

Atanassov, K. (2016). Intuitionistic fuzzy sets. International Journal Bioautomation, 20, 1.

Atanassov, K. T. (1999). Interval valued intuitionistic fuzzy sets. In Intuitionistic Fuzzy Sets (pp. 139-177). Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1870-3_2

Yager, R. R. (2013). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375

Yager, R. R. (2016). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222-1230. https://doi.org/10.1109/TFUZZ.2016.2604005

Joshi, B. P., Singh, A., Bhatt, P. K., & Vaisla, K. S. (2018). Interval valued q-rung orthopair fuzzy sets and their properties. Journal of Intelligent & Fuzzy Systems, 35(5), 5225-5230. https://doi.org/10.3233/JIFS-169806

Liu, P., & Wang, P. (2018). Multiple-attribute decision-making based on Archimedean Bonferroni Operators of q-rung orthopair fuzzy numbers. IEEE Transactions on Fuzzy systems, 27(5), 834-848. https://doi.org/10.1109/TFUZZ.2018.2826452

Liu, P., Chen, S. M., & Wang, P. (2018). Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(10), 3741-3756. https://doi.org/10.1109/TSMC.2018.2852948

Garg, H., & Chen, S. M. (2020). Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets. Information Sciences, 517, 427-447. https://doi.org/10.1016/j.ins.2019.11.035

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

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

Ullah, K., Mahmood, T., Ali, Z., & Jan, N. (2020). On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex & Intelligent Systems, 6, 15-27. https://doi.org/10.1007/s40747-019-0103-6

Liu, P., Ali, Z., & Mahmood, T. (2019). A method to multi-attribute group decision-making problem with complex q-rung orthopair linguistic information based on heronian mean operators. International Journal of Computational Intelligence Systems, 12(2), 1465-1496. https://doi.org/10.2991/ijcis.d.191030.002

Liu, P., Mahmood, T., & Ali, Z. (2020). Complex Q-rung orthopair fuzzy aggregation operators and their applications in multi-attribute group decision making. Information, 11(1), 5. https://doi.org/10.3390/info11010005

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

Rani, D., & Garg, H. (2017). Distance measures between the complex intuitionistic fuzzy sets and their applications to the decision-making process. International Journal for Uncertainty Quantification, 7(5), 423-439. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2017020356

Garg, H., & Rani, D. (2019). A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making. Applied Intelligence, 49(2), 496-512. https://doi.org/10.1007/s10489-018-1290-3

Garg, H., & Rani, D. (2020). Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process. Artificial Intelligence Review, 53, 3595–3620. https://doi.org/10.1007/s10462-019-09772-x

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

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

Garg, H., Ali, Z., & Mahmood, T. Algorithms for complex interval‐valued q‐rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS. Expert Systems, 38(1), e12609. https://doi.org/10.1111/exsy.12609

Garg, H., Gwak, J., Mahmood, T., & Ali, Z. (2020). Power aggregation operators and VIKOR methods for complex q-rung orthopair fuzzy sets and their applications. Mathematics, 8(4), 538. https://doi.org/10.3390/math8040538

Ibrahim, H. Z., & Alshammari, I. (2022). n, m-Rung Orthopair Fuzzy Sets With Applications to Multicriteria Decision Making. IEEE Access, 10, 99562-99572. https://doi.org/10.1109/ACCESS.2022.3207184

Rajput, A. S., Shukla, S., & Thakur, S. S. (2023). Cosine similarity measures of (m, n)-rung orthopair fuzzy sets and their applications in plant leaf disease classification. Symmetry, 15(7), 1385. https://doi.org/10.3390/sym15071385

Ibrahim, H. Z. (2024). Exploring complex n, m-rung orthopair fuzzy aggregation operators for enhanced multi-attribute decision making. Granular Computing, 9(2), 48. https://doi.org/10.1007/s41066-024-00471-9

Published

2025-01-01

How to Cite

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), 113-131. https://doi.org/10.31181/sor21202514