Evaluating E-Commerce Websites under Uncertainty Using a Hybrid Fuzzy Knowledge–Entropy–TODIM Framework

Aanchal; Sonia; Satish Kumar

doi:10.67334/cds31202641

Authors

Aanchal Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana-Ambala 133207, Haryana, India Author https://orcid.org/0009-0005-0335-4052
Sonia Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana-Ambala 133207, Haryana, India Author https://orcid.org/0009-0001-6395-8422
Satish Kumar Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana-Ambala 133207, Haryana, India Author https://orcid.org/0000-0002-7503-9677

DOI:

https://doi.org/10.67334/cds31202641

Keywords:

Fuzzy Knowledge Measure, Triangular Fuzzy Numbers, Entropy Weighting, TODIM, E-Commerce Website Evaluation

Abstract

Assessing the reliability of e-commerce platforms is a challenging task due to the large number of interrelated evaluation criteria and the uncertainty inherent in decision-making data. To address this issue, this study proposes a novel decision-support framework that integrates Triangular Fuzzy Numbers (TFNs), the entropy weighting method, and the TODIM approach. TFNs are employed to model uncertainty in expert assessments, the entropy method determines the objective importance of the evaluation criteria, and TODIM is used to rank the e-commerce platforms. A case study involving five international e-commerce platforms evaluated against eleven criteria demonstrates the applicability of the proposed framework. Its performance is further validated through comparisons with several well-established multi-criteria decision-making (MCDM) methods. In addition, sensitivity analysis using two different approaches confirms the robustness and reliability of the obtained rankings. The results demonstrate that the proposed framework provides consistent and reliable rankings, making it an effective decision-support tool for evaluating the reliability of e-commerce platforms.

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References

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

Zadeh, L. A. (1968). Probability measures of fuzzy events. Journal of mathematical analysis and applications, 23(2), 421–427. https://doi.org/10.1016/0022-247X(68)90078-4 DOI: https://doi.org/10.1016/0022-247X(68)90078-4

Pal, N. R., & Pal, S. K. (1992). Higher order fuzzy entropy and hybrid entropy of a set. Information Sciences, 61(3), 211–231. https://doi.org/10.1016/0020-0255(92)90051-9 DOI: https://doi.org/10.1016/0020-0255(92)90051-9

Arya, V., & Kumar, S. (2020). Fuzzy entropy measure with an applications in decision making under bipolar fuzzy environment based on topsis method. Int J Inf Manag Sci, 31(2), 99–121. https://doi.org/10.6186/IJIMS.202006_31(2).0001

Hooda, D. (2004). On generalized measures of fuzzy entropy. Mathematica slovaca, 54(3), 315–325.

Joshi, R., & Kumar, S. (2018). An (r, s)-norm fuzzy information measure with its applications in multiple-attribute decision-making. Computational and Applied Mathematics, 37(3), 2943–2964. https://doi.org/10.1007/s40314-017-0491-4 DOI: https://doi.org/10.1007/s40314-017-0491-4

Kapur, J. N. (1997). Measures of fuzzy information. Mathematical Sciences Trust Society.

Arya, V., & Kumar, S. (2021). Knowledge measure and entropy: A complementary concept in fuzzy theory. Granular Computing, 6(3), 631–643. https://doi.org/10.1007/s41066-020-00221-7 DOI: https://doi.org/10.1007/s41066-020-00221-7

Kumar, S., et al. (2024). A new exponential knowledge and similarity measure with application in multi-criteria decision-making. Decision Analytics Journal, 10, 100407. https://doi.org/10.1016/j.dajour.2024.100407 DOI: https://doi.org/10.1016/j.dajour.2024.100407

Singh, A., & Kumar, S. (2023). Novel fuzzy knowledge and accuracy measures with its applications in multi-criteria decision-making. Granular Computing, 8(6), 1359–1384. https://doi.org/10.1007/s41066-023-00374-1 DOI: https://doi.org/10.1007/s41066-023-00374-1

Singh, S., Lalotra, S., & Sharma, S. (2019). Dual concepts in fuzzy theory: Entropy and knowledge measure. International Journal of Intelligent Systems, 34(5), 1034–1059. https://doi.org/10.1002/int.22085 DOI: https://doi.org/10.1002/int.22085

Singh, S., Sharma, S., & Ganie, A. H. (2020). On generalized knowledge measure and generalized accuracy measure with applications to madm and pattern recognition. Computational and Applied Mathematics, 39(3), 231. https://doi.org/10.1007/s40314-020-01243-2 DOI: https://doi.org/10.1007/s40314-020-01243-2

Raminpour, S., Weisberg, E. M., Kauffman, L., & Fishman, E. K. (2024). Websites, mobile apps, and social media: Premier online educational tools for radiology. Clinical Imaging, 113, 110239. https://doi.org/10.1016/j.clinimag.2024.110239 DOI: https://doi.org/10.1016/j.clinimag.2024.110239

Hery, Budiman, J., Widjaja, A. E., Haryani, C. A., & Tarigan, R. E. (2024). The development and prototyping of game modeling at a family entertainment center, utilizing web-based arduino technology for calculating cagr. DOI: https://doi.org/10.1016/j.procs.2024.03.080

Miniukovich, A., & Figl, K. (2024). Dataset of user evaluations of prototypicality, aesthetics, usability and trustworthiness of homepages of banking, e-commerce and university websites. Data in Brief, 52, 109976. https://doi.org/10.1016/j.dib.2023.109976 DOI: https://doi.org/10.1016/j.dib.2023.109976

Cheng, Y.-J., & Chen, K.-H. (2023). Website analytics for government user behavior during covid-19 pandemic. Aslib Journal of Information Management, 75(1), 90–111. https://doi.org/10.1108/AJIM-11-2021-0329 DOI: https://doi.org/10.1108/AJIM-11-2021-0329

Uzir, M. U. H., Al Halbusi, H., Thurasamy, R., Hock, R. L. T., Aljaberi, M. A., Hasan, N., & Hamid, M. (2021). The effects of service quality, perceived value and trust in home delivery service personnel on customer satisfaction: Evidence from a developing country. Journal of Retailing and Consumer Services, 63, 102721. https://doi.org/10.1016/j.jretconser.2021.102721 DOI: https://doi.org/10.1016/j.jretconser.2021.102721

Sahoo, S. K., & Goswami, S. S. (2023). A comprehensive review of multiple criteria decision-making (mcdm) methods: Advancements, applications, and future directions. Decision Making Advances, 1(1), 25–48. https://doi.org/10.31181/dma1120237 DOI: https://doi.org/10.31181/dma1120237

Pawełek-Lubera, E., Przyborowski, M., Ślęzak, D., & Wasilewski, A. (2025). Multi-criteria selection of data clustering methods for e-commerce personalization. Applied Soft Computing, 182, 113559. https://doi.org/10.1016/j.asoc.2025.113559 DOI: https://doi.org/10.1016/j.asoc.2025.113559

Varchandi, S., Memari, A., & Jokar, M. R. A. (2024). An integrated best–worst method and fuzzy topsis for resilient-sustainable supplier selection. Decision Analytics Journal, 11, 100488. https://doi.org/10.1016/j.dajour.2024.100488 DOI: https://doi.org/10.1016/j.dajour.2024.100488

de Melo, F. J. C., de Arruda Xavier, L., de Albuquerque, A. P. G., & de Medeiros, D. D. (2023). Evaluation of quality of online shopping services in times of covid-19 based on es-qual model and fuzzy topsis method. Soft Computing, 27(11), 7497–7515. https://doi.org/10.1007/s00500-022-07696-3 DOI: https://doi.org/10.1007/s00500-022-07696-3

Suriya Kumari, D., Manoharan, P. S., Chidambarathanu, K., & Vishnupriyan, J. (2025). Optimization of self-sufficient hybrid renewable energy source fed bwro desalting plant through fuzzy ahp and vikor mcdm techniques. Desalination and Water Treatment, 322, 101215. https://doi.org/10.1016/j.dwt.2025.101215 DOI: https://doi.org/10.1016/j.dwt.2025.101215

Görçün, Ö. F., Chatterjee, P., Aytekin, A., Korucuk, S., & Pamucar, D. (2025). Strategic analysis of e-trade platforms in automotive spare part sector: A t-spherical fuzzy perspective. Journal of Industrial Information Integration, 44, 100782. https://doi.org/10.1016/j.jii.2025.100782 DOI: https://doi.org/10.1016/j.jii.2025.100782

AbdelAziz, N. M., Samy, A., Hussien, G. S., & Naguib, S. (2025). E-commerce website quality evaluation using triangular neutrosophic with todim under uncertainty environment. Neutrosophic Sets and Systems, 90(1), 19. https://doi.org/10.5281/zenodo.16340449

Deli, I., & Subas, Y. (2014). Single valued neutrosophic numbers and their applications to multicriteria decision making problem. Neutrosophic Sets Syst, 2(1), 1–13.

De Luca, A., & Termini, S. (1993). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. In Readings in fuzzy sets for intelligent systems (pp. 197–202). Elsevier. https://doi.org/10.1016/B978-1-4832-1450-4.50020-1 DOI: https://doi.org/10.1016/B978-1-4832-1450-4.50020-1

Bhandari, D., & Pal, N. R. (1993). Some new information measures for fuzzy sets. Information Sciences, 67(3), 209–228. https://doi.org/10.1016/0020-0255(93)90073-U DOI: https://doi.org/10.1016/0020-0255(93)90073-U

Havrda, J., & Charvát, F. (1967). Quantification method of classification processes. concept of structural a-entropy. Kybernetika, 3(1), 30–35.

Singh, S., & Ganie, A. H. (2022). Two-parametric generalized fuzzy knowledge measure and accuracy measure with applications. International Journal of Intelligent Systems, 37(7), 3836–3880. https://doi.org/10.1002/int.22705 DOI: https://doi.org/10.1002/int.22705

Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—i. Information sciences, 8(3), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5 DOI: https://doi.org/10.1016/0020-0255(75)90036-5

Goel, M., & Narain, S. (2025). Fuzzy knowledge and accuracy measures with its applications in e-commerce websites decision making. Palestine Journal of Mathematics, 14(3).

He, D., Xu, J., & Chen, X. (2016). Information-theoretic-entropy based weight aggregation method in multiple-attribute group decision-making. Entropy, 18(6), 171. https://doi.org/10.3390/e18060171 DOI: https://doi.org/10.3390/e18060171

Liu, L., Zhou, J., An, X., Zhang, Y., & Yang, L. (2010). Using fuzzy theory and information entropy for water quality assessment in three gorges region, china. Expert Systems with Applications, 37(3), 2517–2521. https://doi.org/10.1016/j.eswa.2009.08.004 DOI: https://doi.org/10.1016/j.eswa.2009.08.004

Zhu, Y., Tian, D., & Yan, F. (2020). Effectiveness of entropy weight method in decision-making. Mathematical problems in Engineering, 2020(1), 3564835. https://doi.org/10.1155/2020/3564835 DOI: https://doi.org/10.1155/2020/3564835

Gomes, L., & Lima, M. (1991). Todimi: Basics and application to multicriteria ranking. Found. Comput. Decis. Sci, 16(3-4), 1–16.

Yang, G., Ren, M., & Hao, X. (2023). Multi-criteria decision-making problem based on the novel probabilistic hesitant fuzzy entropy and todim method. Alexandria Engineering Journal, 68, 437–451. https://doi.org/10.1016/j.aej.2023.01.014 DOI: https://doi.org/10.1016/j.aej.2023.01.014

Chen, J., & Yin, C. (2024). A new probabilistic linguistic decision-making process based on pl- bwm and improved three-way todim methods. Egyptian Informatics Journal, 28, 100567. https://doi.org/10.1016/j.eij.2024.100567 DOI: https://doi.org/10.1016/j.eij.2024.100567

Ali, J., & Pamucar, D. (2025). Normal wiggly probabilistic hesitant fuzzy-based todim approach for optimal solid waste disposal method selection. Heliyon, 11(2). https://doi.org/10.1016/j.heliyon.2025.e41908 DOI: https://doi.org/10.1016/j.heliyon.2025.e41908

Wang, J., Wei, G., & Lu, M. (2018). Todim method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Symmetry, 10(10), 486. https://doi.org/10.3390/sym10100486 DOI: https://doi.org/10.3390/sym10100486

Bączkiewicz, A. (2021). Mcdm based e-commerce consumer decision support tool. Procedia Computer Science, 192, 4991–5002. https://doi.org/10.1016/j.procs.2021.09.277 DOI: https://doi.org/10.1016/j.procs.2021.09.277

Gupta, S., Kushwaha, P. S., Badhera, U., Chatterjee, P., & Gonzalez, E. D. S. (2023). Identification of benefits, challenges, and pathways in e-commerce industries: An integrated two-phase decision-making model. Sustainable Operations and Computers, 4, 200–218. https://doi.org/10.1016/j.susoc.2023.08.005 DOI: https://doi.org/10.1016/j.susoc.2023.08.005

Cüvelek, G., & Oztaysi, B. (2024). Product performance measurement system for ecommerce by using fuzzy ahp-topsis. International Conference on Intelligent and Fuzzy Systems, 208–217. https://doi.org/10.1007/978-3-031-67195-1_26 DOI: https://doi.org/10.1007/978-3-031-67195-1_26

Seker, S. (2019). Fuzzy ahp-qfd methodology and its application to retail chain. International Conference on Intelligent and Fuzzy Systems, 1189–1197. https://doi.org/10.1007/978-3-030-23756-1_140 DOI: https://doi.org/10.1007/978-3-030-23756-1_140

Kumar, R., Ramesh, J. V. N., Mohanty, S. N., Rafiq, M., Shernazarov, I., & Khan, M. I. (2025). Evaluating consumers benefits in electronic-commerce using fuzzy topsis. Results in Control and Optimization, 18, 100535. https://doi.org/10.1016/j.rico.2025.100535 DOI: https://doi.org/10.1016/j.rico.2025.100535

Juanli, L., Lei, H., Yubo, W., Ye, L., Sleiman, K. A. A., & Suliman, M. A. (2025). An empirical investigation of e-loyalty formation for online shopping in china. Acta Psychologica, 258, 105135. https://doi.org/10.1016/j.actpsy.2025.105135 DOI: https://doi.org/10.1016/j.actpsy.2025.105135

Yu, X., Guo, S., Guo, J., & Huang, X. (2011). Rank b2c e-commerce websites in e-alliance based on ahp and fuzzy topsis. Expert Systems with Applications, 38(4), 3550–3557. https://doi.org/10.1016/j.eswa.2010.08.143 DOI: https://doi.org/10.1016/j.eswa.2010.08.143

Rouyendegh, B. D., Topuz, K., Dag, A., & Oztekin, A. (2019). An ahp-ift integrated model for performance evaluation of e-commerce web sites. Information Systems Frontiers, 21(6), 1345–1355. https://doi.org/10.1007/s10796-018-9825-z DOI: https://doi.org/10.1007/s10796-018-9825-z

Rekik, R. (2019). An integrated fuzzy anp-topsis approach to rank and assess e-commerce web sites. International Conference on Hybrid Intelligent Systems, 197–209. https://doi.org/10.1007/978-3-030-49336-3_20 DOI: https://doi.org/10.1007/978-3-030-49336-3_20

Aydin, S., & Kahraman, C. (2012). Evaluation of e-commerce website quality using fuzzy multicriteria decision making approach. IAENG International Journal of Computer Science, 39(1).

Liu, X., He, M., Gao, F., & Xie, P. (2008). An empirical study of online shopping customer satisfaction in china: A holistic perspective. International Journal of Retail & Distribution Management, 36(11), 919–940. https://doi.org/10.1108/09590550810911683 DOI: https://doi.org/10.1108/09590550810911683

Denguir-Rekik, A., Mauris, G., & Montmain, J. (2006). Propagation of uncertainty by the possibility theory in choquet integral-based decision making: Application to an e-commerce website choice support. IEEE Transactions on Instrumentation and Measurement, 55(3), 721–728. https://doi.org/10.1109/TIM.2006.873803 DOI: https://doi.org/10.1109/TIM.2006.873803

Zavadskas, E. K., Bausys, R., Lescauskiene, I., & Usovaite, A. (2021). Multimoora under interval-valued neutrosophic sets as the basis for the quantitative heuristic evaluation methodology hebin. Mathematics, 9(1), 66. https://doi.org/10.3390/math9010066 DOI: https://doi.org/10.3390/math9010066

Lewis, M. (2006). The effect of shipping fees on customer acquisition, customer retention, and purchase quantities. Journal of Retailing, 82(1), 13–23. https://doi.org/10.1016/j.jretai.2005.11.005 DOI: https://doi.org/10.1016/j.jretai.2005.11.005

Lantz, B., & Hjort, K. (2013). Real e-customer behavioural responses to free delivery and free returns. Electronic Commerce Research, 13(2), 183–198. https://doi.org/10.1007/s10660-013-9125-0 DOI: https://doi.org/10.1007/s10660-013-9125-0

Wang, M. (2003). Assessment of e-service quality via e-satisfaction in e-commerce globalization. The Electronic Journal of Information Systems in Developing Countries, 11(1), 1–4. https://doi.org/10.1002/j.1681-4835.2003.tb00073.x DOI: https://doi.org/10.1002/j.1681-4835.2003.tb00073.x

Satapathy, S., Mahapatra, T. K., Alba-Baena, N., & Mishra, M. (2024). A complete mcdm-based approach for acoustic material selection using the copras tool. In Noise pollution and ergonomic intervention by acoustic material (pp. 21–35). Springer. https://doi.org/10.1007/978-3-031-66308-6_3 DOI: https://doi.org/10.1007/978-3-031-66308-6_3

Brauers, W. K., & Zavadskas, E. K. (2006). The moora method and its application to privatization in a transition economy. Control and cybernetics, 35(2), 445–469.

Zavadskas, E. K., & Turskis, Z. (2010). A new additive ratio assessment (aras) method in multicriteria decision-making. Technological and Economic Development of Economy, 16(2), 159–172. https://doi.org/10.3846/tede.2010.10 DOI: https://doi.org/10.3846/tede.2010.10

Lin, S.-S., Zhou, A., & Shen, S.-L. (2023). Safety assessment of excavation system via topsis-based mcdm modelling in fuzzy environment. Applied Soft Computing, 138, 110206. https://doi.org/10.1016/j.asoc.2023.110206 DOI: https://doi.org/10.1016/j.asoc.2023.110206

Zavadskas, E. K., Antuchevičienė, J., Šaparauskas, J., & Turskis, Z. (2013). Mcdm methods waspas and multimoora: Verification of robustness of methods when assessing alternative solutions. Economic Computation and Economic Cybernetics Studies and Research, 47, 5–20.