Multi-attribute decision-making (MADM) relies heavily on the aggregation of fuzzy data, yet determining the most appropriate decision remains challenging, especially when information is limited or uncertain. To address this, recent research has introduced Aczel-Alsina (AA) aggregation operators (AOs) for different types of fuzzy sets. This study proposes novel Fermatean fuzzy aggregation operators by incorporating AA t-norm and AA t-conorm, along with the development of AA product and AA sum for Fermatean fuzzy sets. Additionally, we introduce two innovative operators: the Fermatean fuzzy AA weighted averaging and Fermatean fuzzy AA weighted geometric operators. The theoretical properties of these operators, including idempotency, monotonicity, and boundedness, are rigorously analyzed. To validate the effectiveness of the proposed approach, we apply it to a decision-making problem in the cross-border e-commerce environment, focusing on AI-driven consumer behavior prediction and personalized targeted advertising campaigns. A global retail firm utilizing AI algorithms to analyze large-scale consumer data is examined as a case study. Our method enhances decision-making by aligning marketing strategies with cultural and consumption patterns across different regions, ultimately improving customer engagement and increasing sales. Comparative analysis with existing methodologies demonstrates that our approach outperforms conventional techniques, offering a more accurate and adaptable decision-making framework. This research contributes to the broader understanding of AI-based personalization in business environments. It reinforces its role as a robust decision-support tool for sustainable and socially responsible global market interactions.
SmithsonMVerkuilenJ. Fuzzy set theory: applications in the social sciences. Thousand Oaks: Sage, 2006.
4.
AtanassovK. Review and new results on intuitionistic fuzzy sets. Int J Bio1988; 20(1): S7–S16. IM-MFAIS-1-88.
5.
AtanassovKT. More on intuitionistic fuzzy sets. Fuzzy Set Syst1989; 33(1): 37–45.
6.
YagerRR. Pythagorean fuzzy subsets. In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS). Edmonton, AB, Canada, 2013, pp. 57–61.
7.
YagerRRAbbasovAM. Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst2013; 28(5): 436–452.
8.
AbdullahLGohP. Decision making method based on Pythagorean fuzzy sets and its application to solid waste management. Complex Intellig Syst2019; 5: 185–198.
9.
ChaurasiyaRJainD. Hybrid MCDM method onthagorean fuzzy set and its application. Decis Mak Appl Manag Eng2023; 6(1): 379–398.
10.
DeschrijverGCornelisCKerreEE. On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Trans Fuzzy Syst2004; 12(1): 45–61.
11.
NganRT. A classification into subclasses of intuitionistic t-norms and t-conorms for intuitionistic fuzzy sets. UED J Soc Sci Hum Edu2016; 6(2): 19–28.
12.
MishraVNKumarTSharmaMK, et al.Pythagorean and fermatean fuzzy sub-group redefined in context of T-norm and S-conorm. J Fuzzy Ext Appl2023; 4(2): 125–135.
WangWLiuX. Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst2011; 26(11): 1049–1075.
15.
PengXYuanH. Fundamental properties of Pythagorean fuzzy aggregation operators. Fundam Inf2016; 147(4): 415–446.
16.
RahmanKAbdullahSGhaniF. Some new generalized interval-valued Pythagorean fuzzy aggregation operators using Einstein t-norm and t-conorm. J Intell Fuzzy Syst2019; 37(3): 3721–3742.
17.
AkramMDudekWADarJM. Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision-making. Int J Intell Syst2019; 34(11): 3000–3019.
18.
KhanAAAshrafSAbdullahS, et al.Pythagorean fuzzy Dombi aggregation operators and their application in decision support system. Symmetry2019; 11(3): 383.
19.
AczelJAlsinaC. Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Aequationes Math1982; 25(1): 313–315.
20.
SenapatiTChenGYagerRR. Aczel–Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making. Int J Intell Syst2022; 37(2): 1529–1551.
21.
SenapatiTChenGMesiarR, et al.Novel Aczel–Alsina operations-based interval-valued intuitionistic fuzzy aggregation operators and their applications in multiple attribute decision-making process. Int J Intell Syst2022; 37(8): 5059–5081.
22.
HussainAUllahKAlshahraniMN, et al.Novel Aczel–Alsina operators for Pythagorean fuzzy sets with application in multi-attribute decision making. Symmetry2022; 14(5): 940.
23.
HussainAUllahKYangMS, et al.Aczel-Alsina aggregation operators on T-spherical fuzzy (TSF) information with application to TSF multi-attribute decision making. IEEE Access2022; 10: 26011–26023.
24.
GargH. Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. Arabian J Sci Eng2017; 42(12): 5275–5290.
25.
WuSJWeiGW. Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J Know Intell Eng Syst2017; 21(3): 189–201.
26.
ZhangX. A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst2016; 31(6): 593–611.
27.
GargHRaniD. Robust averaging–geometric aggregation operators for complex intuitionistic fuzzy sets and their applications to MCDM process. Arabian J Sci Eng2020; 45: 2017–2033.
28.
SeikhMRMandalU. Interval-valued Fermatean fuzzy Dombi aggregation operators and SWARA based PROMETHEE II method to bio-medical waste management. Expert Syst Appl2023; 226: 120082.
29.
SeikhMRChatterjeeP. Determination of best renewable energy sources in India using SWARA-ARAS in confidence level based interval-valued Fermatean fuzzy environment. Appl Soft Comput2024; 155: 111495.
30.
AshrafSKousarMHameedMS. Early infectious diseases identification based on complex probabilistic hesitant fuzzy N-soft information. Soft Comput2023; 27(23): 18285–18310.
31.
AshrafSChohanMSAhmadS, et al.Decision aid algorithm for kidney transplants under disc spherical fuzzy sets with distinctive radii information. IEEE Access2023; 11: 122029–122044.
32.
KamranMAshrafSSalamatN, et al.Smart city design plan selection through single-valued neutrosophic probabilistic hesitant fuzzy rough aggregation information. J Intell Fuzzy Syst2023; 45(6): 1–45.
33.
AshrafSIqbalWHameedMS, et al.An enhanced CRADIS decision model for optimizing radioactive waste reduction through transmutations based on Disc Spherical Fuzzy information. Appl Soft Comput2024; 167: 112289.
34.
XiaMXuZZhuB. Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl Base Syst2012; 31: 78–88.
35.
SarfrazMUllahKAkramM, et al.Prioritized aggregation operators for intuitionistic fuzzy information based on Aczel–Alsina t-norm and t-conorm and their applications in group decision-making. Symmetry2022; 14(12): 2655.
36.
HadiAKhanWKhanA. A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators. Int J Intell Syst2021; 36(7): 3464–3499.
37.
YangHC. Research on ways to revitalize traditional markets by exploring research trends. J Econ Mark Manag2023; 11(4): 53–63.
38.
OvsyannikovaDde MelloVOInzlichtM. Third-party evaluators perceive AI as more compassionate than expert humans. Commun Psychol2025; 3(1): 4.
39.
AgarwalSSharmaSFaisalKN, et al.Time-series forecasting using SVMD-LSTM: a hybrid approach for stock market prediction. J Probab Stat2025; 2025(1): 9464938.
40.
IbrahimNMAbiduzzamanSMRaziffARA, et al.A collaborative filtering approach using machine learning and business intelligence: a critical review. Int J Percept Comput2025; 11(1): 41–49.
41.
NandagopalS. Deep association rule-based dimensionality reduction for big data analytics uncovering complex patterns and improving efficiency. ICTACT J Soft Comput2023; 13(4): 3061–3066.
42.
AlhitmiHKMardiahAAl-SulaitiKI, et al.Data security and privacy concerns of AI-driven marketing in the context of economics and business field: an exploration into possible solutions. Cogent Bus Manag2024; 11(1): 2393743.
43.
EkuerhareAUdokaOP. The effect of globalization on language services and translation strategies. Int J Adv Multidiscip Res Stud2024; 4(6): 507–516.
44.
KaramchandG. The impact of cloud computing on e-commerce scalability and personalization. Aitoz Multidiscip Rev2024; 3(1): 13–18.
45.
SemwalMAkilaKManasaM, et al.Machine learning-enabled business intelligence for dynamic pricing strategies in e-commerce. In: 2024 2nd International Conference on Disruptive Technologies (ICDT). India, Greater Noida, 2024, pp. 116–120.
46.
HussainAUllahKAlshahraniMN, et al.Novel Aczel-Alsina operators for Pythagorean fuzzy sets with application in multi-attribute decision making. Symmetry2022; 14(5): 940.
47.
YinSZhaoY. An agent-based evolutionary system model of the transformation from building material industry (BMI) to green intelligent BMI under supply chain management. Humanit Soc Sci Commun2024; 11(1): 1–15.
48.
YuYYinS. Incentive mechanism for the development of rural new energy industry: new energy enterprise–village collective linkages considering the quantum entanglement and benefit relationship. Int J Energy Res2023; 1: 1–19.
