Abstract
In this modern marketing and technological era, a strong strategy regarding digital marketing is crucial for the development of any organization. Digital marketing strategies are a collection of structured electronic-marketing aspects used by companies to fulfill marketing objectives and clients’ needs. These strategies are necessary for electronic marketing managers and are the best way to increase profits and sales. The basic purpose of this paper is to explore best digital marketing strategies and how they affect client purchasing behavior at online retailers. Linguistic data gathered from clients are protected throughout the collection of data using a fuzzy 2-tuple linguistic (2TL) representation model and its integrated form with q-rung orthopair fuzzy set (q-ROFS), named a 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS) is presented. Moreover, this paper goes a step further by extending the Hamacher operators to power aggregation operators, thereby presenting a comprehensive set of 2TLq-ROF power Hamacher aggregation operators. These advancements and methodologies enable a comprehensive analysis of client data while leveraging the power of fuzzy logic and linguistic modeling techniques, leading to valuable insights into the influence of digital marketing strategies on consumer behavior in the online retail sector. The main feature of the suggested operators is their ability to not only determine the correlations between any number of attributes and consider relationships between membership and non-membership degrees but also provide more general conclusions via a parameter. After defining the multi-attribute group decision-making (MAGDM) approach, we implement the inter-criteria correlation (CRITIC) method for calculating the attribute weights. We also examine a novel strategy for dealing with MAGDM problems based on the presented operators. Last but not least, the suggested method is utilized in a real-world scenario involving the selection of the best digital marketing strategy to demonstrate their applicability and efficacy as well as the influence of parameters on the final results. The advantageous features and novelty of the presented methodology are further demonstrated by a detailed comparison with relevant approaches.
Similar content being viewed by others
Data availability
For inquiries regarding data availability, please contact the authors.
References
Abbad MM (2021) Using the UTAUT model to understand students’ usage of e-learning systems in developing countries. Educ Inf Technol 26(6):7205–7224
Agarwal M (2021) A study on Pay-Per-Click advertising. Asian J Multidimensional Res 10(11):618–624
Akram M, Peng X, Sattar A (2021) A new decision-making model using complex intuitionistic fuzzy Hamacher aggregation operators. Soft Comput 25(10):7059–7086
Akram M, Naz S, Feng F, Shafiq A (2022) Assessment of hydropower plants in Pakistan: Muirhead mean-based 2-tuple linguistic t-spherical fuzzy combining SWARA with COPRAS. Arab J Sci Eng. https://doi.org/10.1007/s13369-022-07081-0
Akram M, Naz S, Santos-Garcia G, Saeed MR (2023) Extended CODAS method for MAGDM with 2-tuple linguistic T-spherical fuzzy sets. AIMS 8(2):3428–3468
Akram M, Niaz Z, Feng F (2023) Extended CODAS method for multi-attribute group decision-making based on 2-tuple linguistic Fermatean fuzzy aggregation operators. Granular Comput. https://doi.org/10.1007/s41066-022-00332-3
Akram M, Shahzadi S, Bibi R, Santos-García G (2023) Extended group decision-making methods with 2-tuple linguistic Fermatean fuzzy sets. Soft Comput. https://doi.org/10.1007/s00500-023-08158-0
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Aydemir SB, Gunduz SY (2021) A novel approach to multi-attribute group decision-making based on power neutrality aggregation operator for \(q\)-rung orthopair fuzzy sets. Int J Intell Syst 36(3):1454–1481
Biswas A, Deb N (2021) Pythagorean fuzzy Schweizer and Sklar power aggregation operators for solving multi-attribute decision-making problems. Granular Comput 6:991–1007
Bu Y, Parkinson J, Thaichon P (2021) Digital content marketing as a catalyst for e-WOM in food tourism. Australas Mark J 29(2):142–154
Chen SJ, Chen SM (2001) A new method to measure the similarity between fuzzy numbers. In 10th IEEE International Conference on Fuzzy Systems (Cat No:01CH37297) (Vol. 3 pp:1123-1126) IEEE
Chen SM, Niou SJ (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872
Chen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Systems 118:204–216
Chen SM, Wang CH (2009) Fuzzy risk analysis based on ranking fuzzy numbers using a-cuts belief features and signal/noise ratios. Expert Appl 36(3):5576–5581
Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Transact Syst Man Cybern Part B (Cybernetics) 40(5):1343
Chen SM, Ko YK, Chang YC, Pan JS (2009) Weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques. IEEE Trans Fuzzy Syst 17(6):1412–1427
Cid-López A, Hornos MJ, Carrasco RA, Herrera-Viedma E, Chiclana F (2017) Linguistic multi-criteria decision-making model with output variable expressive richness. Expert Syst Appl 83:350–362
Diakoulaki D, Mavrotas Papayannakis L (1995) Determining objective weights in multiple criteria problems: The CRITIC method. Comput Res 22(7):763–770
Dong J, Wan S, Chen SM (2021) Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Inf Sci 547:1080–1104
Fahmi A, Maqbool Z, Amin F, Aslam M (2022) Web applications for multiuser interaction based on power Heronian aggregation operators. Soft Comput 26(10):4553–4573
Faizi S, Salabun W, Nawaz S, ur Rehman A, Watróbski J, (2021) Best-Worst method and Hamacher aggregation operations for intuitionistic 2-tuple linguistic sets. Expert Syst Appl 181:115088
Feng F, Zheng Y, Sun B, Akram M (2022) Novel score functions of generalized orthopair fuzzy membership grades with application to multiple decision-making. Granular Comput 7(1):95–111
Forghani E, Sheikh R, Hosseini SMH, Sana SS (2022) The impact of digital marketing strategies on customer’s buying behavior in online the rough set theory. Int J Syst Assur Eng Manag. https://doi.org/10.1007/s13198-021-01315-4
Garg H, Ali Z, Mahmood T (2021) Interval-valued picture uncertain linguistic generalized Hamacher aggregation operators and their application multiple attribute decision-making process. Arab J Sci Eng. https://doi.org/10.1007/s13369-020-05313-9
Gong ZW, Forrest J, Yang YJ (2013) The optimal group consensus models for 2-tuple linguistic preference relations. Knowl-Based Syst 37:427–437
Hadi A, Khan W, Khan A (2021) A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators. Int J Intell Syst 36(7):3464–3499
Hallikainen H, Luongo M, Dhir A, Laukkanen T (2022) Consequences of personalized product recommendations and price promotions in online grocery shopping. J Retail Consum Serv 69:103088
Hamacher H (1975) Ber logische Verknpfungen unscharfer Aussagen und deren zugehrige Bewertungsfunktionen. RWTH Aachen West Germany 75(14)
Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752
Hollebeek LD, Macky K (2019) Digital content marketing’s role in fostering consumer engagement trust and value: Framework fundamental propositions and implications. J Interact Mark 45(1):27–41
Jana C, Pal M (2021) Multi-criteria decision-making process based on some single-valued neutrosophic Dombi power aggregation operators. Soft Comput 25(7):5055–5072
Khan AA, Qiyas M, Abdullah S, Luo J, Bano M (2019) Analysis of robot selection based on 2-tuple picture fuzzy linguistic aggregation. Mathematics 7(10):1000
Kushwaha BP (2020) Search engine marketing a new way of marketing in digital age. PalArch’s J Archaeol Egypt/Egyptol 17(6):2053–2065
Labella Á, Dutta B, Martínez L (2021) An optimal best-worst prioritization method under a 2-tuple linguistic environment in decision-making. Ind Eng 155:107141
Li R (2023) An integrated group decision-making method for brand packaging design effect evaluation based on the 2-tuple linguistic Pythagorean fuzzy sets. J Intell Fuzzy Syst. https://doi.org/10.3233/JIFS-232054
Li CC, Rodríguez RM, Martínez L, Dong Y, Herrera F (2018) Personalized individual semantics based on consistency in hesitant decision-making with comparative linguistic expressions. Knowl-Based Syst 145:156–165
Mu Z, Zeng S, Wang P (2021) Novel approach to multi-attribute group decision-making based on interval-valued Pythagorean fuzzy power symmetric mean operator. Comput Industrial Eng 155:107049
Naz S, Akram M, Al-Shamiri MMA, Saeed MR (2022) Evaluation of network security service provider using 2-tuple linguistic complex-rung COPRAS method. Complexity. https://doi.org/10.1155/2022/4523287
Naz S, Akram M, Muhiuddin G, Shafiq A (2022) Modified EDAS method for MAGDM based on MSM operators with 2-tuple linguistic-spherical fuzzy sets. Math Problems Eng. https://doi.org/10.1155/2022/5075998
Naz S, Akram M, Saeid AB, Saadat A (2022) Models for MAGDM with dual hesitant \(q\)-rung orthopair fuzzy 2-tuple linguistic MSM operators and application to COVID-19 pandemic. Expert Syst 39(8):e13005. https://doi.org/10.1111/exsy.13005
Naz S, Akram M, Sattar A, Al-Shamiri MMA (2022) 2-tuple linguistic \(q\)-rung orthopair fuzzy CODAS approach and its application in arc welding selection. AIMS Math 7(9):17529–17569
Qiyas M, Abdullah S, Ashraf S, Khan S, Khan A (2019) Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision-making problems. Math Foundations Comput 2(3):183
Rawat SS, Komal, (2022) Multiple attribute decision-making based on \(q\)-rung orthopair fuzzy Hamacher Muirhead mean operators. Soft Comput 26(5):2465–2487
Shen CW, Luong TH, Ho JT, Djailani I (2020) Social media marketing of IT service companies: analysis using a concept-linking mining Mark. Manage 90:593–604
Simic V, Gokasar I, Deveci M, Karakurt A (2022) An integrated CRITIC and MABAC based type-2 neutrosophic model for public transportation pricing system selection. Socioecon Plann Sci 80:101157. https://doi.org/10.1016/j.seps.2021.101157
Tong X, Lai KH, Zhu Q, Zhao S, Chen J, Cheng TCE (2018) Multinational enterprise buyers’ choices for extending corporate social to suppliers in emerging countries: A multi-method study. J Oper Manag 63:25–43
Verma R, Álvarez-Miranda E (2023) Group decision-making method based on advanced aggregation operators with entropy and divergence measures under 2-tuple linguistic Pythagorean fuzzy environment. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2023.120584
Wang W, Liu X (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst 26(11):1049–1075
Wang L, Garg H, Li N (2021) Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight. Soft Comput 25(2):973–993
Wang W, Tian G, Zhang T, Jabarullah NH, Li F, Fathollahi-Fard AM, Li Z (2021) Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory. J Clean Prod 281:124724
Xu Z (2004) A method based on linguistic aggregation operators for group decision-making with linguistic preference relations. Inf Sci 166(1–4):19–30
Xu Z, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433
Xu Z, Yager RR (2009) Power-geometric operators and their use in group decision-making. IEEE Trans Fuzzy Syst 18(1):94–105
Xu W, Shang X, Wang J (2021) Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean. Complex Intell Syst 7(3):1673–1693
Yager RR (2001) The power average operator. IEEE Transact Syst Man Cybern-Part A Syst Hum 31(6):724–731
Yager RR (2013) Pythagorean membership grades in multi-criteria decision-making. IEEE Trans Fuzzy System 22(4):958–965
Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230
Zadeh LA (1975) Fuzzy logic and approximate reasoning. Synthese 30(3):407–428
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249
Zeng S, Qiyas M, Arif M, Mahmood T (2019) Extended version of linguistic picture fuzzy TOPSIS method and its applications in enterprise resource planning systems. Math Problems Eng. https://doi.org/10.1155/2019/8594938
Zeng S, Hu Y, Xie X (2021) \(q\)-Rung orthopair fuzzy weighted induced logarithmic distance measures and their application in multiple attribute decision-making. Eng Appl Artif Intell 100:104167
Zhang C, Bai W, Li D, Zhan J (2022) Multiple attribute group decision-making based on multigranulation probabilistic models MULTIMOORA and TPOP incomplete \(q\)-rung orthopair fuzzy information systems. Int J Approximate Reason 143:102–120
Zhang H, Wei G, Chen X (2022) Spherical fuzzy Dombi power Heronian mean aggregation operators for multiple attribute group decision-making. Comput Appl Math 41(3):1–54
Zhao H, Xu Z, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30
Zhao M, Wei G, Wu J, Guo Y, Wei C (2021) TODIM method for multiple attribute group decision-making based on cumulative prospect theory with linguistic neutrosophic sets. Int J Intell Syst 36(3):1199–1222
Funding
The authors have not provided information on the funding sources for this study.
Author information
Authors and Affiliations
Contributions
All authors have equal contribution.
Corresponding author
Ethics declarations
Conflict of interest
The authors state that they have no conflicts of interest.
Ethical approval
This article does not involve any studies with human participants or animals conducted by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Naz, S., Fatima, S.S., Butt, S.A. et al. A MAGDM model based on 2-tuple linguistic variables and power Hamacher aggregation operators for optimal selection of digital marketing strategies. Granul. Comput. 8, 1955–1990 (2023). https://doi.org/10.1007/s41066-023-00408-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41066-023-00408-8