Fermatean Fuzzy CRADIS Approach Based on Triangular Divergence for Selecting Online Shopping Platform
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
Mijanur Rahaman Seikh
1
,
Arnab Mukherjee
2
1 - Department of Mathematics, Kazi Nazrul University, Asansol, 713340, India.
2 - Department of Mathematics, Kazi Nazrul University, Asansol, 713340, India.
کلید واژه: Multi-attribute decision-making, Fermatean fuzzy set, Distance measure, CRADIS, Triangular divergence, Online shopping platform selection.,
چکیده مقاله :
As the digital landscape continues to evolve, the selection of an appropriate online shop-ping platform has become increasingly crucial for both consumers and businesses. This paper introduces a novel approach that combines the Fermatean fuzzy set theory with the triangular divergence distance measure in Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS) method to streamline the decision-making process in online platform selection. Through a comprehensive example, we illustrate the application of this approach in evaluating and ranking four distinct online shopping latforms based on multiple criteria. Through this integrated approach, decision-makers can gain valuable insights into the rela-tive merits of each online shopping platform, allowing them to make informed choices aligned with their preferences and requirements. Furthermore, by accommodating uncertainty and imprecision, the Fermatean fuzzy set theory enhances the robustness of the decision-making process, minimizing the risk of making suboptimal decisions. Overall, this paper demon-strates the practical applicability of Fermatean fuzzy set theory in decision support systems for online platform selection. To demonstrate the proposed method’s applicability, we have compared the results with existing Multi-attribute decision making (MADM) methods. To establish its stability, we conducted a sensitivity analysis. By leveraging the CRADIS method alongside Fermatean fuzzy set theory, decision-makers can navigate the complex landscape of online shopping platforms with greater confidence and efficiency, ultimately leading to more satisfactory outcomes for both consumers and businessesalike.
As the digital landscape continues to evolve, the selection of an appropriate online shop-ping platform has become increasingly crucial for both consumers and businesses. This paper introduces a novel approach that combines the Fermatean fuzzy set theory with the triangular divergence distance measure in Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS) method to streamline the decision-making process in online platform selection. Through a comprehensive example, we illustrate the application of this approach in evaluating and ranking four distinct online shopping latforms based on multiple criteria. Through this integrated approach, decision-makers can gain valuable insights into the rela-tive merits of each online shopping platform, allowing them to make informed choices aligned with their preferences and requirements. Furthermore, by accommodating uncertainty and imprecision, the Fermatean fuzzy set theory enhances the robustness of the decision-making process, minimizing the risk of making suboptimal decisions. Overall, this paper demon-strates the practical applicability of Fermatean fuzzy set theory in decision support systems for online platform selection. To demonstrate the proposed method’s applicability, we have compared the results with existing Multi-attribute decision making (MADM) methods. To establish its stability, we conducted a sensitivity analysis. By leveraging the CRADIS method alongside Fermatean fuzzy set theory, decision-makers can navigate the complex landscape of online shopping platforms with greater confidence and efficiency, ultimately leading to more satisfactory outcomes for both consumers and businessesalike.
[1] Ali J. Norm-based distance measure of q-rung orthopair fuzzy sets and its application in decision-making. Computational and Applied Mathematics. 2023; 42(4): 184. DOI: https://doi.org/10.1007/s40314-023-02313-x
[2] Ali J. Spherical fuzzy symmetric point criterion-based approach using Aczel-Alsina prioritization: Application to sustainable supplier selection. Granular Computing. 2024; 9(2): 33. DOI: https://doi.org/10.1007/s41066-024-00449-7
[3] Ali J, Bashir Z, Rashid T. On distance measure and TOPSIS model for probabilistic interval-valued hesitant fuzzy sets: Application to healthcare facilities in public hospitals. Grey Systems: Theory and Application. 2022; 12(1): 197-229. DOI: https://doi.org/10.1108/GS-07-2020-0092
[4] Ali J, Garg H. On spherical fuzzy distance measure and TAOV method for decision-making problems with incomplete weight information. Engineering Applications of Artificial Intelligence. 2023; 119: 105726. DOI: https://doi.org/10.1016/j.engappai.2022.105726
[5] Das S, Roy BK, Kar MB, Kar S, Pamucar D. Neutrosophic fuzzy set and its application in decision making. Journal of Ambient Intelligence and umanized Computing. 2020; 11: 5017-5029. DOI: https://doi.org/10.1007/s12652-020-01808-3
[6] Deng Z, Wang J. New distance measure for Fermatean fuzzy sets and its application. International Journal of Intelligent Systems. 2022; 37(3): 1903-1930. DOI: https://doi.org/10.1002/int.22760
[7] Ejegwa PA, Muhiuddin G, Algehyne EA, Agbetayo JM, Al-Kadi D. An enhanced Fermatean fuzzy composition relation based on a maximum-average approach and its application in diagnostic analysis. Journal of Mathematics. 2022; 2022(1): 1786221. DOI: https://doi.org/10.1155/2022/1786221
[8] Ejegwa PA, Sarkar A. Fermatean fuzzy approach of diseases diagnosis based on new correlation coefficient operators. In: Deep Learning in Personalized Healthcare and Decision Support. Academic Press. 2023. p.23-38. DOI: https://doi.org/10.1016/B978-0-443-19413-9.00021-7
[9] Ejegwa PA, Wanzenke TD, Ogwuche IO, Anum MT, Isife KI. A robust correlation coefficient for Fermatean fuzzy sets based on spearman’s correlation measure with application to clustering and selection process. Journal of Applied Mathematics and Computing. 2024; 70(2): 1747-1770. DOI:
https://doi.org/10.1007/s12190-024-02019-1
[10] Ejegwa PA, Zuakwagh D. Fermatean fuzzy modified composite relation and its application in pattern recognition. Journal of Fuzzy Extension and Applications. 2022; 3(2): 140-151. DOI: https://doi.org/10.22105/jfea.2022.335251.1210
[11] Ganie AH, Singh S. An innovative picture fuzzy distance measure and novel multi-attribute decisionmaking method. Complex & Intelligent Systems. 2021; 7: 781-805. DOI: https://doi.org/10.1007/s40747-020-00235-3
[12] G¨ul S. Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID-19 testing laboratory selection problem. Expert Systems. 2021; 38(8): e12769. DOI: https://doi.org/10.1111/exsy.12769
[13] Jayakumar V, Kannan J, Kausar N, Deveci M, Wen X. Multicriteria group decision making for prioritizing IoT risk factors with linear Diophantine fuzzy sets and MARCOS method. Granular Computing. 2024; 9(3): 56. DOI: https://doi.org/10.1007/s41066-024-00480-8
[14] Kirisci M. New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach. Knowledge and Information Systems. 2023; 65(2): 855-868. DOI: https://doi.org/10.1007/s10115-022-01776-4
[15] Krishankumar R, Ecer F. Selection of IoT service provider for sustainable transport using q-rung orthopair fuzzy CRADIS and unknown weights. Applied Soft Computing. 2023; 132: 109870. DOI: https://doi.org/10.1016/j.asoc.2022.109870
[16] Liu Z. A distance measure of Fermatean fuzzy sets based on triangular divergence and its application in medical diagnosis. Journal of Operations Intelligence. 2024; 2(1): 167-178. DOI: https://doi.org/10.31181/jopi21202415
[17] Mandal U, Seikh MR. Interval-valued Fermatean fuzzy TOPSIS method and its application to sustainable development program. In: Congress on Intelligent Systems: Proceedings of CIS 2021, Springer Nature, Singapore. 2022. p.783-796. DOI: https://doi.org/10.1007/978-981-16-9113-3_57
[18] Mishra AR, Chen SM, Rani P. Multiattribute decision making based on Fermatean hesitant fuzzy sets and modified VIKOR method. Information Sciences. 2022; 607: 1532-1549. DOI: https://doi.org/10.1016/j.ins.2022.06.037
[19] Onyeke IC, Ejegwa PA. Modified Senapati and Yager’s Fermatean fuzzy distance and its application in students’ course placement in tertiary institution. In: Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, Springer,
Singapore. 2022. p.237-253. DOI: https://doi.org/10.1007/978-981-19-4929-6_11
[20] Palanikumar M, Kausar N, Garg H, Ahmed SF, Samaniego C. Robot sensors process based on generalized Fermatean normal different aggregation operators framework. Aims Mathematics. 2023; 8(7): 16252-16277. DOI: https://doi.org/10.3934/math.2023832
[21] Palanikumar M, Kausar N, Pamucar D, Kar S, Kim C, Nam Y. Novelty of different distance approach for multi-criteria decision-making challenges using q-rung vague sets. Computer Modeling in Engineering & Sciences. 2024; 139(3): 3353-3385. DOI: https://doi.org/10.32604/cmes.2024.031439
[22] Puˇska A, Stevic Zˇ, Pamucar D. Evaluation and selection of healthcare waste incinerators using extended sustainability criteria and multi-criteria analysis methods. Environment, Development and Sustainability. 2022; 24: 11195-11225. DOI: https://doi.org/10.1007/s10668-021-01902-2
[23] Puˇska A, Sˇtilic A, Stevic Zˇ. A comprehensive decision framework for selecting distribution center locations: A hybrid improved fuzzy SWARA and fuzzy CRADIS approach. Computation. 2023; 11(4): 73. DOI: https://doi.org/10.3390/computation11040073
[24] Puˇska A, Stojanovic I. Fuzzy multi-criteria analyses on green supplier selection in an agri-food company. Journal of Intelligent Management Decision. 2022; 1(1): 2-16. DOI: https://doi.org/10.56578/jimd010102
[25] Sahoo L. Similarity measures for Fermatean fuzzy sets and its applications in group decision-making. Decision Science Letters. 2022; 11(2): 167-180. DOI: https://doi.org/10.5267/dsl.2021.11.003
[26] Seikh MR, Chatterjee P. Determination of best renewable energy sources in India using SWARA-ARAS in confidence level based interval-valued Fermatean fuzzy environment. Applied Soft Computing. 2024; 155: 111495. DOI: https://doi.org/10.1016/j.asoc.2024.111495
[27] Seikh MR, Mandal U. Multiple attribute decision-making based on 3,4-quasirung fuzzy sets. Granular Compututing. 2022; 7: 965-978. DOI: https://doi.org/10.1007/s41066-021-00308-9
[28] Seikh MR, Mandal U. Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem. Engineering Applications of Artificial Intelligence. 2022; 115: 105299. DOI: https://doi.org/10.1016/j.engappai.2022.105299
[29] Seikh MR, Mandal U. Interval-valued Fermatean fuzzy Dombi aggregation operators and SWARA based PROMETHEE II method to bio-medical waste management. Expert Systems with Applications. 2023; 226: 120082. DOI: https://doi.org/10.1016/j.eswa.2023.120082
[30] Senapati T, Yager RR. Fermatean fuzzy sets. Journal of Ambient Intelligence and Humanized Computing. 2020; 11: 663-674. DOI: https://doi.org/10.1007/s12652-019-01377-0
[31] Surya AN, Vimala J, Kausar N, Stevic Z, Shah MA. Entropy for q-rung linear diophantine fuzzy hypersoft set with its application in MADM. Scientific Reports. 2024; 14(1): 5770. DOI: https://doi.org/10.1038/s41598-024-56252-6
[32] Torra V. Hesitant fuzzy sets. International Journal of Intelligent Systems. 2010; 25(6): 529-539. DOI: https://doi.org/10.1002/int.20418
[33] Yehudayoff A. Pointer chasing via triangular discrimination. Combinatorics, Probability and Computing. 2020; 29(4): 485-494. DOI: https://doi.org/10.1017/S0963548320000085
[34] Yuan J, Chen Z, Wu M. A novel distance measure and CRADIS method in Picture fuzzy environment. International Journal of Computational Intelligence Systems. 2023; 16(1): 186. DOI: https://doi.org/10.1007/s44196-023-00354-y
[35] Zuakwagh D, Ejegwa PA, Akwu AD. Fermatean fuzzy sets in multiset framework with application in diagnostic process based on composite relations. In: Strategic Fuzzy Extensions and Decision-making Techniques. CRC Press; 2024. p.195-210. DOI: https://doi.org/10.1201/9781003497219
