Revolutionizing Decision-Making in E-Commerce and IT Procurement: An IVPNS-COBRA Linguistic Variable Framework for Enhanced Multi-Criteria Analysis

Samsiah Abdul Razak; Zahari Md Rodzi; Faisal Al-Sharqi; Nazirah Ramli

doi:10.31181/ijes1412025176

Authors

Samsiah Abdul Razak College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Cawangan Perak, Kampus Tapah, 35400 Tapah Road, Perak, Malaysia Author https://orcid.org/0009-0000-2510-0719
Zahari Md Rodzi College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia Author https://orcid.org/0000-0003-4145-3340
Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Author https://orcid.org/0000-0002-2574-3703
Nazirah Ramli College of Computing, Informatics and Mathematics Universiti Teknologi Mara Cawangan Pahang, Kampus Jengka 26400 Bandar Jengka Pahang , Malaysia Author https://orcid.org/0000-0001-8800-7431

DOI:

https://doi.org/10.31181/ijes1412025176

Keywords:

Interval-valued Pythagorean Neutrosophic set, IVPNS, Comprehensive Distance Based Ranking, COBRA, linguistic variable, Euclidean distance, Hamming distance

Abstract

Real-world challenges in e-commerce strategy selection and IT supplier evaluation are inherently complex due to uncertainty and incomplete information, necessitating a multi-faceted approach for effective decision-making. Traditional single methods often fail to address these complexities adequately. To overcome this limitation, this research introduces an advanced methodology by integrating the Interval-Valued Pythagorean Neutrosophic Set (IVPNS) with the Comprehensive Distance-Based Ranking (COBRA) approach, enhancing the handling of indeterminate information related to truth, falsity, and uncertainty. IVPNS provides a robust mathematical framework for managing ambiguity, a common challenge in Multi-Criteria Decision-Making (MCDM) across various domains. Prior to this study, IVPNS lacked a linguistic variable—a crucial component for expressing human judgments. To bridge this gap, we enhance the IVPNS-COBRA framework by incorporating 5-point and 7-point linguistic scales, ensuring compliance with established IVPNS conditions. Additionally, we introduce two distance measures, Euclidean and Hamming distances, to refine alternative evaluations. The proposed IVPNS-COBRA method is validated through real-world applications, including the evaluation of three e-commerce development strategies (assessed against five criteria) and four IT supplier selection alternatives (evaluated using nine criteria). The results demonstrate the reliability of this MCDM model, providing decision-makers with a more precise and structured approach for selecting optimal e-commerce strategies and IT suppliers in complex environments.

Downloads

Download data is not yet available.

References

Laudon, K. C., & Traver, C. G. (2021). E-Commerce: Business, Technology, Society Global edition. 17th edition. E-ISBN: 978-1-292-40932-0

McAfee, A. & Brynjolfsson, E., (2014). The second machine age: Work, progress, and prosperity in a time of brilliant technologies. WW Norton & company.

Briandana, R., & Mihardja, E. J. (2020). Consumer Journey and Social Media: The Content Management Of E-Catering Marketplace Promotion Media for Same Catering Services Business Industry. International Journal Of Communication Research, 10(1).

Boadu, K., & Achiaa, A. (2019). Customer relationship management and customer retention. Customer Relationship Management and Customer Retention (October 20, 2019). https://dx.doi.org/10.2139/ssrn.3472492

Dewan, R., Jing, B., & Seidmann, A. (2000). Adoption of Internet-based product customization and pricing strategies. Journal of Management Information Systems, 17(2), 9-28. https://doi.org/10.1080/07421222.2000.11045644

Timmers, P. (1998). Business models for electronic markets. Electronic markets, 8(2), 3-8. https://doi.org/10.1080/10196789800000016.

Williamson, O. E. (2010). Transaction cost economics: The natural progression. American Economic Review, 100(3), 673-690. https://doi.org/10.1257/aer.100.3.673

Kumar, D., & Rahman, Z. (2015). Sustainability adoption through buyer supplier relationship across supply chain: A literature review and conceptual framework. International Strategic Management Review, 3(1–2), 110–127. https://doi.org/10.1016/j.ism.2015.04.002

Razak, S. A., Ramli, N., Azmi, M. I. H. N., Nor, M. I. M., & Noreddie, H. A. H. (2024, September). Fuzzy Topsis with Ratings Based on Sub-Criteria for Selection of Supplier. In 2024 5th International Conference on Artificial Intelligence and Data Sciences (AiDAS) (pp. 1-5). IEEE. https://doi.org/10.1109/AiDAS63860.2024.10730581.

Sobhanallahi, M. A., Zendehdel Nobari, N., & Pasandideh, S. H. R. (2019). An aggregated supplier selection method based on QFD and TOPSIS (case study: A financial institution). Journal of optimization in industrial engineering, 12(1), 31-40.

Taghipour, A., Rouyendegh, B. D., Ünal, A., & Piya, S. (2022). Selection of suppliers for speech recognition products in IT projects by combining techniques with an integrated fuzzy MCDM. Sustainability, 14(3), 1777. https://doi.org/10.3390/su14031777

Jana, P. (2020). Supplier selection under strategic decision environment. Independent Journal of Management & Production, 11(1), 065-080. https://doi.org/10.14807/ijmp.v11i1.1018.

Smarandache, F., Hassan, A., Malik, M., Bakali, A., & Talea, M. (2017). Special types of bipolar single valued neutrosophic graphs. Annals of Fuzzy Mathematics and Informatics, 14(1), 55-73. https://doi.org/10.30948/afmi.2017.14.1.55

Zhang, Q., Hu, J., Feng, J., Liu, A., & Li, Y. (2019). New similarity measures of pythagorean fuzzy sets and their applications. IEEE Access, 7, 138192-138202. https://doi.org/10.1109/access.2019.2942766.

Yang, W., Wang, C., Liu, Y., & Sun, Y. (2019). Hesitant pythagorean fuzzy interaction aggregation operators and their application in multiple attribute decision-making. Complex & Intelligent Systems, 5(2), 199-216. https://doi.org/10.1007/s40747-019-0104-5.

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.2307/2272014

Turksen, I. B. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy sets and systems, 20(2), 191-210. https://doi.org/10.1016/0165-0114(86)90077-1

Atanassov, K. T. (1986). Intuitionistic fuzzy sets theory. Fuzzy sets and systems, PP. 87-96. https://doi.org/10.1007/978-3-7908-1870-3_1

Atanassov, K. T., & Atanassov, K. T. (1999). Interval valued intuitionistic fuzzy sets. Intuitionistic fuzzy sets: Theory and applications, 139-177. https://doi.org/10.1007/978-3-7908-1870-3_2

Ye, J. (2016). Correlation coefficients of interval neutrosophic hesitant fuzzy sets and its application in a multiple attribute decision making method. Informatica, 27(1), 179-202. http://dx.doi.org/10.15388/Informatica.2016.81

Iryna, S., Zhong, Y., Jiang, W., Deng, X., & Geng, J. (2020). Single-valued neutrosophic set correlation coefficient and its application in fault diagnosis. Symmetry, 12(8), 1371. https://doi.org/10.3390/sym12081371

Smarandache, F., Abdel-Basser, M., & Broumi, S. (Eds.). (2021). Neutrosophic Sets and Systems, Vol. 46, 2021. Infinite Study.

Ebenanjar, P. E., Immaculate, H. J., & Wilfred, C. B. (2018, December). On neutrosophic b-open sets in neutrosophic topological space. In Journal of Physics: Conference Series (Vol. 1139, No. 1, p. 012062). IOP Publishing. https://doi.org/ 10.1088/1742-6596/1139/1/012062

Uluçay, V., Şahin, M., & Hassan, N. (2018). Generalized neutrosophic soft expert set for multiple-criteria decision-making. Symmetry, 10(10), 437. https://doi.org/10.3390/sym10100437

Asghar, A., Hussain, A., Ahmad, K., Ishtiaq, U., Al Sulami, H., & Hussain, N. (2023). On neutrosophic 2-metric spaces with application. Journal of Function Spaces, 2023. https://doi.org/10.1155/2023/9057107

Al-Tahan, M., Davvaz, B., & Parimala, M. (2020). A note on single valued neutrosophic sets in ordered groupoids. International Journal of Neutrosophic Science (IJNS), 10(2), 73-83. https://doi.org/10.5281/zenodo.4001964

Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Interval valued neutrosophic graphs. Critical Review, XII, 2016, 5-33.

Nanthini, T., & Pushpalatha, A. (2020). Interval Valued Neutrosophic Topological Spaces. Neutrosophic Sets and Systems, 32(1), 52-60.

Broumi, S., Deli, I., & Smarandache, F. (2015). N-valued interval neutrosophic sets and their application in medical diagnosis. Critical Review, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA, 10, 45-69.

Gayen, S., Smarandache, F., Jha, S., & Kumar, R. (2020). Interval-valued neutrosophic subgroup based on interval-valued triple t-norm. In Neutrosophic sets in decision analysis and operations research (pp. 215-243). IGI Global. https://doi.org/10.4018/978-1-7998-2555-5.ch010

Zhang, Q., Hu, J., Feng, J., Liu, A., & Li, Y. (2019). New similarity measures of Pythagorean fuzzy sets and their applications. IEEe Access, 7, 138192-138202. DOI:10.1109/ACCESS.2019.2942766

Arthi, N. and Mohana, K. (2021). A new divergence measure of interval-valued pythagorean fuzzy sets and its application. Journal of Computational Mathematica, 5(2), 9-24. https://doi.org/10.26524/cm103.

Antonia, S., & Mohana, K. (2021). Correlation measure for interval valued pythagorean fuzzy sets. Journal of Computational Mathematica, 5(1), 48-59. https://doi.org/10.26524/cm91

Chinnadurai, V., & Selvam, A. (2020). Interval valued Pythagorean fuzzy ideals in semigroups. Journal of Fuzzy Extension and Applications, 1(4), 293-303. https://doi.org/10.22105/jfea.2020.252687.1023

Du, Y., Hou, F., Zafar, W., Yu, Q., & Zhai, Y. (2017). A novel method for multiattribute decision making with interval‐valued Pythagorean fuzzy linguistic information. International Journal of Intelligent Systems, 32(10), 1085-1112. https://doi.org/10.1002/int.21881

Gou, L., & Zhong, Y. (2019). A new fault diagnosis method based on attributes weighted neutrosophic set. IEEE Access, 7, 117740-117748. http://dx.doi.org/10.1109/ACCESS.2019.2936494

Haq, R. S. U., Saeed, M., Mateen, N., Siddiqui, F., & Ahmed, S. (2023). An interval-valued neutrosophic based MAIRCA method for sustainable material selection. Engineering Applications of Artificial Intelligence, 123, 106177. https://doi.org/10.1016/j.engappai.2023.106177

Ismail, J. N., Rodzi, Z., Al-Sharqi, F., Hashim, H., & Sulaiman, N. H. (2023). The integrated novel framework: linguistic variables in pythagorean neutrosophic set with DEMATEL for enhanced decision support. Int. J. Neutrosophic Sci, 21(2), 129-141. https://doi.org/10.54216/IJNS.210212

Kamari, M. S. M., Rodzi, Z. M., & Kamis, N. H. (2025). Pythagorean Neutrosophic Method Based on the Removal Effects of Criteria (PNMEREC): An Innovative Approach for Establishing Objective Weights in Multi-Criteria Decision-Making Challenges. Malaysian Journal of Fundamental and Applied Sciences, 21(1), 1678-1696. https://doi.org/10.11113/mjfas.v21n1.3600

Biswas, A., Gazi, K. H., Bhaduri, P., & Mondal, S. P. (2024). Neutrosophic fuzzy decision-making framework for site selection. Journal of Decision Analytics and Intelligent Computing, 4(1),187- 215.https://doi.org/10.31181/jdaic10004122024b

Basuri, T., Gazi, K. H., Bhaduri, P., Das, S. G., & Mondal, S. P. (2025). Decision-analytics-based Sustainable Location Problem-Neutrosophic CRITIC-COPRAS Assessment Model. Management Science Advances, 2(1), 19-58. https://doi.org/10.31181/msa2120257

Abdalla, M. E. M., Uzair, A., Ishtiaq, A., Tahir, M., & Kamran, M. (2025). Algebraic Structures and Practical Implications of Interval-Valued Fermatean Neutrosophic Super HyperSoft Sets in Healthcare. Spectrum of Operational Research, 2(1), 199-218. https://doi.org/10.31181/sor21202523

Krstić, M., Agnusdei, G. P., Miglietta, P. P., Tadić, S., & Roso, V. (2022). Applicability of industry 4.0 technologies in the reverse logistics: a circular economy approach based on comprehensive distance-based ranking (COBRA) method. Sustainability, 14(9), 5632. https://doi.org/10.3390/su14095632

Popović, G., Pucar, Đ., & Smarandache, F. (2022). MEREC-COBRA approach in e-commerce development strategy selection. Journal of process management and new technologies, 10(3-4), 66-74. https://doi.org/10.5937/jpmnt10-41073

Prema, R., & Radha, R. (2022). Generalized neutrosophic pythagorean set. International research journal of modernization in engineering technology and science, 11, 1571-1575. https://www.doi.org/10.56726/IRJMETS31596

Razak, S. A., Rodzi, Z. M., Ahmad, N., & Ahmad, G. (2024). Exploring The Boundaries of Uncertainty: Interval Valued Pythagorean Neutrosophic Set and Their Properties. Malaysian Journal of Fundamental and Applied Sciences, 20(4), 813-824. https://doi.org/10.11113/mjfas.v20n4.3482

Al-Quran, A., Hashim, H., & Abdullah, L. (2020). A hybrid approach of interval neutrosophic vague sets and DEMATEL with new linguistic variable. Symmetry, 12(2), 275. https://doi.org/10.3390/sym12020275

Rahim, N., Abdullah, L., & Yusoff, B. (2020). A border approximation area approach considering bipolar neutrosophic linguistic variable for sustainable energy selection. Sustainability, 12(10), 3971. https://doi.org/10.3390/su12103971

Karabašević, D., Stanujkić, D., Zavadskas, E. K., Stanimirović, P., Popović, G., Predić, B., & Ulutaş, A. (2020). A novel extension of the TOPSIS method adapted for the use of single-valued neutrosophic sets and hamming distance for e-commerce development strategies selection. Symmetry, 12(8), 1263. https://doi.org/10.3390/sym12081263

Yager, R. R. (1980). A linguistic variable for importance of fuzzy sets. Cybernetics and System, 10(1-3), 249-260. https://doi.org/10.1080/01969728008927636

Biswas, P., Pramanik, S., & Giri, B. C. (2016). TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural computing and Applications, 27, 727-737. https://doi.org/10.1007/s00521-015-1891-2

Kamacı, H. (2021). Linguistic single‐valued neutrosophic soft sets with applications in game theory. International Journal of Intelligent Systems, 36(8), 3917-3960. https://doi.org/10.1002/int.22445

Shohaimay, F., Ramli, N., & Mohamed, S. R. (2012, December). Fuzzy evaluation in IT supplier selection. In 2012 International Symposium on Computer Applications and Industrial Electronics (ISCAIE) (pp. 94-98). IEEE. https://doi.org/10.1109/ISCAIE.2012.6482076