EDAS method for multiple attribute group decision making with probabilistic dual hesitant fuzzy information and its application to suppliers selection
Abstract
Probabilistic dual hesitant fuzzy set (PDHFS) is a more powerful and important tool to describe uncertain information regarded as generalization of hesitant fuzzy set (HFS) and dual HFS (DHFS), not only reflects the hesitant attitude of decision-makers (DMs), but also reflects the probability information of DMs. Score function of fuzzy number and weighting method are very important in multi-attribute group decision-making (MAGDM) issues. In many fuzzy environments, the score function and entropy measure have been proposed one after another. Firstly, based on the detailed analysis of the existed score function of PDHF element (PDHFE) and with the help of previous references, we build a novel score function for PDHFE. Secondly, a combined weighting method is built based on the minimum identification information principle by fusing PDHF entropy and Criteria Importance Through Intercriteria Correlation (CRITIC) method. Thirdly, a novel PDHF MAGDM approach (PDHF-EDAS) is built by extending evaluation based on distance from average solution (EDAS) approach to the PDHF environment to solve the issue that the decision attribute information is PDHFE. Finally, the practicability and effectiveness of the PDHF MAGDM technique is verified by suppliers selection (SS) and comparing analysis with existing methods.
First published online 23 January 2023
Keyword : multi-attribute group decision-making, probabilistic dual hesitant fuzzy set, EDAS method, entropy measure, CRITIC method, suppliers selection
How to Cite
Ning, B., Lin, R., Wei, G., & Chen, X. (2023). EDAS method for multiple attribute group decision making with probabilistic dual hesitant fuzzy information and its application to suppliers selection. Technological and Economic Development of Economy, 29(2), 326–352. https://doi.org/10.3846/tede.2023.17589
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Anees, J., Zhang, H. C., Baig, S., Lougou, B. G., & Bona, T. G. R. (2020). Hesitant fuzzy entropy-based opportunistic clustering and data fusion algorithm for heterogeneous wireless sensor networks. Sensors, 20(3), 913. https://doi.org/10.3390/s20030913
Atanassov, K., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33(1), 37–45. https://doi.org/10.1016/0165-0114(89)90215-7
Darko, A. P., & Liang, D. C. (2020). Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Engineering Applications of Artificial Intelligence, 87, 103259. https://doi.org/10.1016/j.engappai.2019.103259
Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763–770. https://doi.org/10.1016/0305-0548(94)00059-H
Fan, J. P., Jia, X. F., & Wu, M. Q. (2020). A new multi-criteria group decision model based on Single-valued triangular Neutrosophic sets and EDAS method. Journal of Intelligent & Fuzzy Systems, 38(2), 2089–2102. https://doi.org/10.3233/JIFS-190811
Garg, H., & Kaur, G. (2018). Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision-making based on aggregation operators with new distance measures. Mathematics, 6(12), 280. https://doi.org/10.3390/math6120280
Garg, H., & Kaur, G. (2020a). Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Computers & Industrial Engineering, 140, 106211. https://doi.org/10.1016/j.cie.2019.106211
Garg, H., & Kaur, G. (2020b). A robust correlation coefficient for probabilistic dual hesitant fuzzy sets and its applications. Neural Computing & Applications, 32, 8847–8866. https://doi.org/10.1007/s00521-019-04362-y
Garg, H., & Kaur, G. (2021). Algorithms for screening travelers during Covid-19 outbreak using probabilistic dual hesitant values based on bipartite graph theory. Applied and Computational Mathematics, 20(1), 22–48.
Haktanir, E., & Kahraman, C. (2021). A Novel CRITIC based weighted FMEA method: Application to COVID-19 blood testing process. Journal of Multiple-Valued Logic and Soft Computing, 37(3–4), 247–275.
Hao, Z. N., Xu, Z. S., Zhao, H., & Su, Z. (2017). Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowledge-Based Systems, 127, 16–28. https://doi.org/10.1016/j.knosys.2017.02.033
Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746–752. https://doi.org/10.1109/91.890332
Huang, M. J., & Li, K. W. (2013). A novel approach to characterizing hesitations in intuitionistic fuzzy numbers. Journal of Systems Science and Systems Engineering, 22, 283–294. https://doi.org/10.1007/s11518-013-5213-x
Huang, Y., Lin, R., & Chen, X. (2021). An enhancement EDAS method based on prospect theory. Technological and Economic Development of Economy, 27(5), 1019–1038. https://doi.org/10.3846/tede.2021.15038
Hwang, C. L., & Yoon, K. P. (1981). Lecture notes in economics and mathematical systems: Vol. 186. Multiple attribute decision making: Methods and applications a state-of-the-art survey. Springer. https://doi.org/10.1007/978-3-642-48318-9
Jiang, Z., Wei, G., & Chen, X. (2022a). EDAS method based on cumulative prospect theory for multiple attribute group decision-making under picture fuzzy environment. Journal of Intelligent & Fuzzy Systems, 42(3), 1723–1735. https://doi.org/10.3233/JIFS-211171
Jiang, Z., Wei, G., & Guo, Y. (2022b). Picture fuzzy MABAC method based on prospect theory for multiple attribute group decision making and its application to suppliers selection. Journal of Intelligent & Fuzzy Systems, 42(4), 3405–3415. https://doi.org/10.3233/JIFS-211359
Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of Evaluation Based on Distance from Average Solution (EDAS). Informatica, 26(3), 435–451. https://doi.org/10.15388/Informatica.2015.57
Krishankumar, R., Garg, H., Arun, K., Saha, A., Ravichandran, K. S., & Kar, S. (2021). An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information. Complex & Intelligent Systems, 7, 2281–2298. https://doi.org/10.1007/s40747-021-00387-w
Lei, F., Wei, G., Shen, W., & Guo, Y. (2022). PDHL-EDAS method for multiple attribute group decision making and its application to 3D printer selection. Technological and Economic Development of Economy, 28(1), 179–200. https://doi.org/10.3846/tede.2021.15884
Li, X., Ju, Y. B., Ju, D. W., Zhang, W. K., Dong, P. W., & Wang, A. H. (2019). Multi-attribute group decision making method based on EDAS under picture fuzzy environment. IEEE Access, 7, 141179–141192. https://doi.org/10.1109/ACCESS.2019.2943348
Liang, Z. W., Liu, X. C., Ye, B. Y., & Wang, Y. J. (2013). Performance investigation of fitting algorithms in surface micro-topography grinding processes based on multi-dimensional fuzzy relation set. International Journal of Advanced Manufacturing Technology, 67, 2779–2798. https://doi.org/10.1007/s00170-012-4692-0
Liao, N., Gao, H., Wei, G., & Chen, X. (2021). CPT-MABAC-based multiple attribute group decision making method with probabilistic hesitant fuzzy information. Journal of Intelligent & Fuzzy Systems, 41(6), 6999–7014. https://doi.org/10.3233/JIFS-210889
Lima, A., Palmeira, E. S., Bedregal, B., & Bustince, H. (2021). Multidimensional fuzzy sets. IEEE Transactions on Fuzzy Systems, 29(8), 2195–2208. https://doi.org/10.1109/TFUZZ.2020.2994997
Liu, X. D., Wang, Z. W., Zhang, S. T., & Garg, H. (2021). An approach to probabilistic hesitant fuzzy risky multiattribute decision making with unknown probability information. International Journal of Intelligent Systems, 36(10), 5714–5740. https://doi.org/10.1002/int.22527
Lu, J., Zhang, S., Wu, J., & Wei, Y. (2021). COPRAS method for multiple attribute group decision making under picture fuzzy environment and their application to green supplier selection. Technological and Economic Development of Economy, 27(2), 369–385. https://doi.org/10.3846/tede.2021.14211
Narayanamoorthy, S., Ramya, L., Kang, D., Baleanu, D., Kureethara, J. V., & Annapoorani, V. (2021). A new extension of hesitant fuzzy set: An application to an offshore wind turbine technology selection process. IET Renewable Power Generation, 15(15), 2340–2355. https://doi.org/10.1049/rpg2.12168
Ning, B., Wei, G., Lin, R., & Guo, Y. (2022). A novel MADM technique based on extended power generalized Maclaurin symmetric mean operators under probabilistic dual hesitant fuzzy setting and its application to sustainable suppliers selection. Expert Systems with Applications, 204, 117419. https://doi.org/10.1016/j.eswa.2022.117419
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445–455. https://doi.org/10.1016/S0377-2217(03)00020-1
Peng, X. D., & Garg, H. (2022). Intuitionistic fuzzy soft decision making method based on CoCoSo and CRITIC for CCN cache placement strategy selection. Artificial Intelligence Review, 55, 1567–1604. https://doi.org/10.1007/s10462-021-09995-x
Pramanik, R., Baidya, D. K., & Dhang, N. (2021). Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory. Frontiers of Structural and Civil Engineering, 15, 478–489. https://doi.org/10.1007/s11709-021-0698-8
Rahimi, M., Kumar, P., Moomivand, B., & Yari, G. (2021). An intuitionistic fuzzy entropy approach for supplier selection. Complex & Intelligent Systems, 7, 1869–1876. https://doi.org/10.1007/s40747-020-00224-6
Ren, Z. L., Xu, Z. S., & Wang, H. (2017, December). An extended TODIM method under probabilistic dual hesitant fuzzy information and its application on enterprise strategic assessment. In 2017 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM) (pp. 1464–1468). Singapore. IEEE. https://doi.org/10.1109/IEEM.2017.8290136
Saraji, M. K., Streimikiene, D., & Kyriakopoulos, G. L. (2021). Fermatean fuzzy CRITIC-COPRAS method for evaluating the challenges to Industry 4.0 adoption for a sustainable digital transformation. Sustainability, 13(17), 9577. https://doi.org/10.3390/su13179577
Shi, H. T., Li, Y. F., Jiang, Z. N., & Zhang, J. (2021). Comprehensive power quality evaluation method of microgrid with dynamic weighting based on CRITIC. Measurement & Control, 54(5–6), 1097–1104. https://doi.org/10.1177/00202940211016092
Su, Y., Zhao, M., Wei, G., Wei, C., & Chen, X. (2022). Probabilistic uncertain linguistic EDAS method based on prospect theory for multiple attribute group decision-making and its application to green finance. International Journal of Fuzzy Systems, 24, 1318–1331. https://doi.org/10.1007/s40815-021-01184-w
Thao, N. X., & Smarandache, F. (2019). A new fuzzy entropy on Pythagorean fuzzy sets. Journal of Intelligent & Fuzzy Systems, 37(1), 1065–1074. https://doi.org/10.3233/JIFS-182540
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539. https://doi.org/10.1002/int.20418
Wang, S., Wei, G., Lu, J., Wu, J., Wei, C., & Chen, X. (2022). GRP and CRITIC method for probabilistic uncertain linguistic MAGDM and its application to site selection of hospital constructions. Soft Computing, 26, 237–251. https://doi.org/10.1007/s00500-021-06429-2
William-West, T. O., & Ciucci, D. (2021). Decision-theoretic five-way approximation of fuzzy sets. Information Sciences, 572, 200–222. https://doi.org/10.1016/j.ins.2021.04.105
Xu, T. T., Zhang, H., & Li, B. Q. (2020). Pythagorean fuzzy entropy and its application in multiple-criteria decision-making. International Journal of Fuzzy Systems, 22, 1552–1564. https://doi.org/10.1007/s40815-020-00877-y
Xu, Z. S., & Zhou, W. (2017). Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optimization and Decision Making, 16, 481–503. https://doi.org/10.1007/s10700-016-9257-5
Yahya, M., Naeem, M., Abdullah, S., Qiyas, M., & Aamir, M. (2021). A novel approach on the intuitionistic fuzzy rough frank aggregation operator-based EDAS method for multicriteria group decision-making. Complexity, 2021, 5534381. https://doi.org/10.1155/2021/5534381
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zafar, S., Alamgir, Z., & Rehman, M. H. (2021). An effective blockchain evaluation system based on entropy-CRITIC weight method and MCDM techniques. Peer-to-Peer Networking and Applications, 14, 3110–3123. https://doi.org/10.1007/s12083-021-01173-8
Zhang, C., Li, D. Y., Liang, J. Y., & Wang, B. L. (2021a). MAGDM-oriented dual hesitant fuzzy multigranulation probabilistic models based on MULTIMOORA. International Journal of Machine Learning and Cybernetics, 12, 1219–1241. https://doi.org/10.1007/s13042-020-01230-3
Zhang, D., Su, Y., Zhao, M., & Chen, X. (2022a). CPT-TODIM method for interval neutrosophic MAGDM and its application to third-party logistics service providers selection. Technological and Economic Development of Economy, 28(1), 201–219. https://doi.org/10.3846/tede.2021.15758
Zhang, H., Wei, G., & Chen, X. (2022b). SF-GRA method based on cumulative prospect theory for multiple attribute group decision making and its application to emergency supplies supplier selection. Engineering Applications of Artificial Intelligence, 110, 104679. https://doi.org/10.1016/j.engappai.2022.104679
Zhang, H. M. (2020). Distance and entropy measures for dual hesitant fuzzy sets. Computational & Applied Mathematics, 39, 91. https://doi.org/10.1007/s40314-020-1111-2
Zhang, H. Y., Wei, G. W., & Chen, X. D. (2022c). Spherical fuzzy Dombi power Heronian mean aggregation operators for multiple attribute group decision-making. Computational & Applied Mathematics, 41, 98. https://doi.org/10.1007/s40314-022-01785-7
Zhang, H. Y., Wei, G. W., & Wei, C. (2022d). TOPSIS method for spherical fuzzy MAGDM based on cumulative prospect theory and combined weights and its application to residential location. Journal of Intelligent & Fuzzy Systems, 42(3), 1367–1380. https://doi.org/10.3233/JIFS-210267
Zhang, S., Gao, H., Wei, G., & Chen, X. (2021b). Grey relational analysis method based on cumulative prospect theory for intuitionistic fuzzy multi-attribute group decision making. Journal of Intelligent & Fuzzy Systems, 41(2), 3783–3795. https://doi.org/10.3233/JIFS-211461
Zhao, M., Gao, H., Wei, G., Wei, C., & Guo, Y. (2022). Model for network security service provider selection with probabilistic uncertain linguistic TODIM method based on prospect theory. Technological and Economic Development of Economy, 28(3), 638–654. https://doi.org/10.3846/tede.2022.16483
Zhao, M., Wei, G., Chen, X., & Wei, Y. (2021a). Intuitionistic fuzzy MABAC method based on cumulative prospect theory for multiple attribute group decision making. International Journal of Intelligent Systems, 36(11), 6337–6359. https://doi.org/10.1002/int.22552
Zhao, M., Wei, G., Guo, Y., & Chen, X. (2021b). CPT-TODIM method for interval-valued bipolar fuzzy multiple attribute group decision making and application to industrial control security service provider selection. Technological and Economic Development of Economy, 27(5), 1186–1206. https://doi.org/10.3846/tede.2021.15044
Zhao, Q., Ju, Y. B., & Pedrycz, W. (2020). A method based on bivariate almost stochastic dominance for multiple criteria group decision making with probabilistic dual hesitant fuzzy information. IEEE Access, 8, 203769–203786. https://doi.org/10.1109/ACCESS.2020.3035906
Zhu, B., Xu., Z., & Xia, M. (2012). Dual hesitant fuzzy sets. Journal of Applied Mathematics, 2012, 2607–2645. https://doi.org/10.1155/2012/879629
Atanassov, K., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33(1), 37–45. https://doi.org/10.1016/0165-0114(89)90215-7
Darko, A. P., & Liang, D. C. (2020). Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Engineering Applications of Artificial Intelligence, 87, 103259. https://doi.org/10.1016/j.engappai.2019.103259
Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763–770. https://doi.org/10.1016/0305-0548(94)00059-H
Fan, J. P., Jia, X. F., & Wu, M. Q. (2020). A new multi-criteria group decision model based on Single-valued triangular Neutrosophic sets and EDAS method. Journal of Intelligent & Fuzzy Systems, 38(2), 2089–2102. https://doi.org/10.3233/JIFS-190811
Garg, H., & Kaur, G. (2018). Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision-making based on aggregation operators with new distance measures. Mathematics, 6(12), 280. https://doi.org/10.3390/math6120280
Garg, H., & Kaur, G. (2020a). Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Computers & Industrial Engineering, 140, 106211. https://doi.org/10.1016/j.cie.2019.106211
Garg, H., & Kaur, G. (2020b). A robust correlation coefficient for probabilistic dual hesitant fuzzy sets and its applications. Neural Computing & Applications, 32, 8847–8866. https://doi.org/10.1007/s00521-019-04362-y
Garg, H., & Kaur, G. (2021). Algorithms for screening travelers during Covid-19 outbreak using probabilistic dual hesitant values based on bipartite graph theory. Applied and Computational Mathematics, 20(1), 22–48.
Haktanir, E., & Kahraman, C. (2021). A Novel CRITIC based weighted FMEA method: Application to COVID-19 blood testing process. Journal of Multiple-Valued Logic and Soft Computing, 37(3–4), 247–275.
Hao, Z. N., Xu, Z. S., Zhao, H., & Su, Z. (2017). Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowledge-Based Systems, 127, 16–28. https://doi.org/10.1016/j.knosys.2017.02.033
Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746–752. https://doi.org/10.1109/91.890332
Huang, M. J., & Li, K. W. (2013). A novel approach to characterizing hesitations in intuitionistic fuzzy numbers. Journal of Systems Science and Systems Engineering, 22, 283–294. https://doi.org/10.1007/s11518-013-5213-x
Huang, Y., Lin, R., & Chen, X. (2021). An enhancement EDAS method based on prospect theory. Technological and Economic Development of Economy, 27(5), 1019–1038. https://doi.org/10.3846/tede.2021.15038
Hwang, C. L., & Yoon, K. P. (1981). Lecture notes in economics and mathematical systems: Vol. 186. Multiple attribute decision making: Methods and applications a state-of-the-art survey. Springer. https://doi.org/10.1007/978-3-642-48318-9
Jiang, Z., Wei, G., & Chen, X. (2022a). EDAS method based on cumulative prospect theory for multiple attribute group decision-making under picture fuzzy environment. Journal of Intelligent & Fuzzy Systems, 42(3), 1723–1735. https://doi.org/10.3233/JIFS-211171
Jiang, Z., Wei, G., & Guo, Y. (2022b). Picture fuzzy MABAC method based on prospect theory for multiple attribute group decision making and its application to suppliers selection. Journal of Intelligent & Fuzzy Systems, 42(4), 3405–3415. https://doi.org/10.3233/JIFS-211359
Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of Evaluation Based on Distance from Average Solution (EDAS). Informatica, 26(3), 435–451. https://doi.org/10.15388/Informatica.2015.57
Krishankumar, R., Garg, H., Arun, K., Saha, A., Ravichandran, K. S., & Kar, S. (2021). An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information. Complex & Intelligent Systems, 7, 2281–2298. https://doi.org/10.1007/s40747-021-00387-w
Lei, F., Wei, G., Shen, W., & Guo, Y. (2022). PDHL-EDAS method for multiple attribute group decision making and its application to 3D printer selection. Technological and Economic Development of Economy, 28(1), 179–200. https://doi.org/10.3846/tede.2021.15884
Li, X., Ju, Y. B., Ju, D. W., Zhang, W. K., Dong, P. W., & Wang, A. H. (2019). Multi-attribute group decision making method based on EDAS under picture fuzzy environment. IEEE Access, 7, 141179–141192. https://doi.org/10.1109/ACCESS.2019.2943348
Liang, Z. W., Liu, X. C., Ye, B. Y., & Wang, Y. J. (2013). Performance investigation of fitting algorithms in surface micro-topography grinding processes based on multi-dimensional fuzzy relation set. International Journal of Advanced Manufacturing Technology, 67, 2779–2798. https://doi.org/10.1007/s00170-012-4692-0
Liao, N., Gao, H., Wei, G., & Chen, X. (2021). CPT-MABAC-based multiple attribute group decision making method with probabilistic hesitant fuzzy information. Journal of Intelligent & Fuzzy Systems, 41(6), 6999–7014. https://doi.org/10.3233/JIFS-210889
Lima, A., Palmeira, E. S., Bedregal, B., & Bustince, H. (2021). Multidimensional fuzzy sets. IEEE Transactions on Fuzzy Systems, 29(8), 2195–2208. https://doi.org/10.1109/TFUZZ.2020.2994997
Liu, X. D., Wang, Z. W., Zhang, S. T., & Garg, H. (2021). An approach to probabilistic hesitant fuzzy risky multiattribute decision making with unknown probability information. International Journal of Intelligent Systems, 36(10), 5714–5740. https://doi.org/10.1002/int.22527
Lu, J., Zhang, S., Wu, J., & Wei, Y. (2021). COPRAS method for multiple attribute group decision making under picture fuzzy environment and their application to green supplier selection. Technological and Economic Development of Economy, 27(2), 369–385. https://doi.org/10.3846/tede.2021.14211
Narayanamoorthy, S., Ramya, L., Kang, D., Baleanu, D., Kureethara, J. V., & Annapoorani, V. (2021). A new extension of hesitant fuzzy set: An application to an offshore wind turbine technology selection process. IET Renewable Power Generation, 15(15), 2340–2355. https://doi.org/10.1049/rpg2.12168
Ning, B., Wei, G., Lin, R., & Guo, Y. (2022). A novel MADM technique based on extended power generalized Maclaurin symmetric mean operators under probabilistic dual hesitant fuzzy setting and its application to sustainable suppliers selection. Expert Systems with Applications, 204, 117419. https://doi.org/10.1016/j.eswa.2022.117419
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445–455. https://doi.org/10.1016/S0377-2217(03)00020-1
Peng, X. D., & Garg, H. (2022). Intuitionistic fuzzy soft decision making method based on CoCoSo and CRITIC for CCN cache placement strategy selection. Artificial Intelligence Review, 55, 1567–1604. https://doi.org/10.1007/s10462-021-09995-x
Pramanik, R., Baidya, D. K., & Dhang, N. (2021). Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory. Frontiers of Structural and Civil Engineering, 15, 478–489. https://doi.org/10.1007/s11709-021-0698-8
Rahimi, M., Kumar, P., Moomivand, B., & Yari, G. (2021). An intuitionistic fuzzy entropy approach for supplier selection. Complex & Intelligent Systems, 7, 1869–1876. https://doi.org/10.1007/s40747-020-00224-6
Ren, Z. L., Xu, Z. S., & Wang, H. (2017, December). An extended TODIM method under probabilistic dual hesitant fuzzy information and its application on enterprise strategic assessment. In 2017 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM) (pp. 1464–1468). Singapore. IEEE. https://doi.org/10.1109/IEEM.2017.8290136
Saraji, M. K., Streimikiene, D., & Kyriakopoulos, G. L. (2021). Fermatean fuzzy CRITIC-COPRAS method for evaluating the challenges to Industry 4.0 adoption for a sustainable digital transformation. Sustainability, 13(17), 9577. https://doi.org/10.3390/su13179577
Shi, H. T., Li, Y. F., Jiang, Z. N., & Zhang, J. (2021). Comprehensive power quality evaluation method of microgrid with dynamic weighting based on CRITIC. Measurement & Control, 54(5–6), 1097–1104. https://doi.org/10.1177/00202940211016092
Su, Y., Zhao, M., Wei, G., Wei, C., & Chen, X. (2022). Probabilistic uncertain linguistic EDAS method based on prospect theory for multiple attribute group decision-making and its application to green finance. International Journal of Fuzzy Systems, 24, 1318–1331. https://doi.org/10.1007/s40815-021-01184-w
Thao, N. X., & Smarandache, F. (2019). A new fuzzy entropy on Pythagorean fuzzy sets. Journal of Intelligent & Fuzzy Systems, 37(1), 1065–1074. https://doi.org/10.3233/JIFS-182540
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539. https://doi.org/10.1002/int.20418
Wang, S., Wei, G., Lu, J., Wu, J., Wei, C., & Chen, X. (2022). GRP and CRITIC method for probabilistic uncertain linguistic MAGDM and its application to site selection of hospital constructions. Soft Computing, 26, 237–251. https://doi.org/10.1007/s00500-021-06429-2
William-West, T. O., & Ciucci, D. (2021). Decision-theoretic five-way approximation of fuzzy sets. Information Sciences, 572, 200–222. https://doi.org/10.1016/j.ins.2021.04.105
Xu, T. T., Zhang, H., & Li, B. Q. (2020). Pythagorean fuzzy entropy and its application in multiple-criteria decision-making. International Journal of Fuzzy Systems, 22, 1552–1564. https://doi.org/10.1007/s40815-020-00877-y
Xu, Z. S., & Zhou, W. (2017). Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optimization and Decision Making, 16, 481–503. https://doi.org/10.1007/s10700-016-9257-5
Yahya, M., Naeem, M., Abdullah, S., Qiyas, M., & Aamir, M. (2021). A novel approach on the intuitionistic fuzzy rough frank aggregation operator-based EDAS method for multicriteria group decision-making. Complexity, 2021, 5534381. https://doi.org/10.1155/2021/5534381
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zafar, S., Alamgir, Z., & Rehman, M. H. (2021). An effective blockchain evaluation system based on entropy-CRITIC weight method and MCDM techniques. Peer-to-Peer Networking and Applications, 14, 3110–3123. https://doi.org/10.1007/s12083-021-01173-8
Zhang, C., Li, D. Y., Liang, J. Y., & Wang, B. L. (2021a). MAGDM-oriented dual hesitant fuzzy multigranulation probabilistic models based on MULTIMOORA. International Journal of Machine Learning and Cybernetics, 12, 1219–1241. https://doi.org/10.1007/s13042-020-01230-3
Zhang, D., Su, Y., Zhao, M., & Chen, X. (2022a). CPT-TODIM method for interval neutrosophic MAGDM and its application to third-party logistics service providers selection. Technological and Economic Development of Economy, 28(1), 201–219. https://doi.org/10.3846/tede.2021.15758
Zhang, H., Wei, G., & Chen, X. (2022b). SF-GRA method based on cumulative prospect theory for multiple attribute group decision making and its application to emergency supplies supplier selection. Engineering Applications of Artificial Intelligence, 110, 104679. https://doi.org/10.1016/j.engappai.2022.104679
Zhang, H. M. (2020). Distance and entropy measures for dual hesitant fuzzy sets. Computational & Applied Mathematics, 39, 91. https://doi.org/10.1007/s40314-020-1111-2
Zhang, H. Y., Wei, G. W., & Chen, X. D. (2022c). Spherical fuzzy Dombi power Heronian mean aggregation operators for multiple attribute group decision-making. Computational & Applied Mathematics, 41, 98. https://doi.org/10.1007/s40314-022-01785-7
Zhang, H. Y., Wei, G. W., & Wei, C. (2022d). TOPSIS method for spherical fuzzy MAGDM based on cumulative prospect theory and combined weights and its application to residential location. Journal of Intelligent & Fuzzy Systems, 42(3), 1367–1380. https://doi.org/10.3233/JIFS-210267
Zhang, S., Gao, H., Wei, G., & Chen, X. (2021b). Grey relational analysis method based on cumulative prospect theory for intuitionistic fuzzy multi-attribute group decision making. Journal of Intelligent & Fuzzy Systems, 41(2), 3783–3795. https://doi.org/10.3233/JIFS-211461
Zhao, M., Gao, H., Wei, G., Wei, C., & Guo, Y. (2022). Model for network security service provider selection with probabilistic uncertain linguistic TODIM method based on prospect theory. Technological and Economic Development of Economy, 28(3), 638–654. https://doi.org/10.3846/tede.2022.16483
Zhao, M., Wei, G., Chen, X., & Wei, Y. (2021a). Intuitionistic fuzzy MABAC method based on cumulative prospect theory for multiple attribute group decision making. International Journal of Intelligent Systems, 36(11), 6337–6359. https://doi.org/10.1002/int.22552
Zhao, M., Wei, G., Guo, Y., & Chen, X. (2021b). CPT-TODIM method for interval-valued bipolar fuzzy multiple attribute group decision making and application to industrial control security service provider selection. Technological and Economic Development of Economy, 27(5), 1186–1206. https://doi.org/10.3846/tede.2021.15044
Zhao, Q., Ju, Y. B., & Pedrycz, W. (2020). A method based on bivariate almost stochastic dominance for multiple criteria group decision making with probabilistic dual hesitant fuzzy information. IEEE Access, 8, 203769–203786. https://doi.org/10.1109/ACCESS.2020.3035906
Zhu, B., Xu., Z., & Xia, M. (2012). Dual hesitant fuzzy sets. Journal of Applied Mathematics, 2012, 2607–2645. https://doi.org/10.1155/2012/879629