Investment decision making along the B&R using critic approach in probabilistic hesitant fuzzy environment
The Belt and Road (B&R) Initiative receives enthusiastic response, the aim of which is to develop cooperative partnerships with countries along the routes and build a community of common destiny. So far, Chinese companies have invested in many different countries along the B&R. Generally, the investment decision making problems are characterized by high risk and uncertainty. Then how to make an appropriate investment decision will be a thorny issue. In this paper, probabilistic hesitant fuzzy set (PHFS) is used for handling uncertainty in multiple attribute decision making (MADM), and the criteria importance through intercriteria correlation (CRITIC) approach is extended to obtain attribute weights, no matter whether the weight information is incompletely known or not. Considering that the existing probabilistic hesitant fuzzy distance measures fail to meet the condition of distance measure, a new distance between PHFSs is proposed and applied to investment decision making for countries along the B&R. In the last, comparative analyses are performed to illustrate the advantages of the presented approach.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Bolturk, E. (2018). Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm. Journal of Enterprise Information Management, 31(4), 550–564. https://doi.org/10.1108/JEIM-01-2018-0020
Deng, H., Yeh, C. H., & Willis, R. J. (2000). Inter-company comparison using modified TOPSIS with objective weights. Computers & Operations Research, 27(10), 963–973. https://doi.org/10.1016/S0305-0548(99)00069-6
Di, Y. N., & You, L. Q. (2018). Investment motives, distance factors and location choice of China’s investment along the Belt and Road. China Soft Science, 2, 168–176.
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
Ding, J., Xu, Z. S., & Zhao, N. (2017). An interactive approach to probabilistic hesitant fuzzy multiattribute group decision making with incomplete weight information. Journal of Intelligent & Fuzzy Systems, 32(3), 2523–2536. https://doi.org/10.3233/JIFS-16503
Duan, F., Ji, Q., Liu, B. Y., & Fan, Y. (2018). Energy investment risk assessment for nations along China’s Belt & Road Initiative. Journal of Cleaner Production, 170, 535–547. https://doi.org/10.1016/j.jclepro.2017.09.152
Gao, J., Xu, Z. S., & Liao, H. C. (2017). A dynamic reference point method for emergency response under hesitant probabilistic fuzzy environment. International Journal of Fuzzy Systems, 19(5), 1261– 1278. https://doi.org/10.1007/s40815-017-0311-4
Grzegorzewski, P. (2004). Distance between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 148(2), 319–328. https://doi.org/10.1016/j.fss.2003.08.005
Hatzimichailidis, A. G., Papakostas, G. A., & Kaburlasos, V. G. (2012). A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. International Journal of Intelligent Systems, 27(4), 396–409. https://doi.org/10.1002/int.21529
Horsky, D., & Rao, M. R. (1984). Estimation of attribute weights from preference comparisons, Management Sciences, 30, 801–822. https://doi.org/10.1287/mnsc.30.7.801
Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision-making: Methods and applications. Springer. https://doi.org/10.1007/978-3-642-48318-9
Kim, S. H., Choi, S. H., & Kim, J. K. (1999). An interactive procedure for multiple attribute group decision making with incomplete information: range-based approach. European Journal of Operational Research, 118(1), 139–152. https://doi.org/10.1016/S0377-2217(98)00309-9
Li, D. Q., & Zeng, W. Y. (2018). Distance measure of Pythagorean fuzzy sets. International Journal of Intelligent Systems, 33(2), 348–361. https://doi.org/10.1002/int.21934
Li, D. Q., Zeng, W. Y., & Zhao, Y. B. (2015). Note on distance measure of hesitant fuzzy sets. Information Sciences, 321, 103–115. https://doi.org/10.1016/j.ins.2015.03.076
Li, J., & Wang, J. Q. (2017). An extended QUALIFLEX method under probability hesitant fuzzy environment for selecting green suppliers. International Journal of Fuzzy Systems, 19, 1866–1879. https://doi.org/10.1007/s40815-017-0310-5
Li, J., & Wang, Z. X. (2018). Consensus building for probabilistic hesitant fuzzy preference relations with expected additive consistency. International Journal of Fuzzy Systems, 20(5), 1495–1510. https://doi.org/10.1007/s40815-018-0451-1
Liu, X. D., Wang, Z. W., & Hetzler, A. (2017). HFMADM method based on nondimensionalization and its application in the evaluation of inclusive growth. Journal of Business Economics and Management, 18(4), 726–744. https://doi.org/10.3846/16111699.2017.1341848
Liu, X. D., Wang, Z. W., Zhang, S. T., & Hetzler, A. (2018). CRM-based dynamic decision-making with hesitant fuzzy information for the evaluation of rangelands. Technological and Economic Development of Economy, 24(5), 1979–2002. https://doi.org/10.3846/tede.2018.5837
Liu, X. D., Wang, Z. W., Zhang, S. T., & Liu, J. S. (2019). Analysis of influencing factors in emergency management based on an integrated methodology. Adaptive Behavior, 27(5), 331–345. https://doi.org/10.1177/1059712319858623
Ma, J., Fan, Z. P., & Huang, L. H. (1999). A subjective and objective integrated approach to determine attribute weights. European Journal of Operational Research, 112(2), 397–404. https://doi.org/10.1016/S0377-2217(98)00141-6
Park, K. S., & Kim, S. H. (1997). Tools for interactive multi-attribute decision making with incompletely identified information. European Journal of Operational Research, 98(1), 111–123. https://doi.org/10.1016/0377-2217(95)00121-2
Singh, P. (2014). Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems. Frontiers of Computer Science, 8, 741–752. https://doi.org/10.1007/s11704-014-3323-3
Song, C. Y., Xu, Z. S., & Zhao, H. (2019). New correlation coefficients between probabilistic hesitant fuzzy sets and their applications in cluster analysis. International Journal of Fuzzy Systems, 21(2), 355–368. https://doi.org/10.1007/s40815-018-0578-0
Su, Z., Xu, Z. S., Zhao, H., Hao, Z. N., & Chen, B. (2019). Entropy measures for probabilistic hesitant fuzzy information. IEEE Access, 7, 65714–65727. https://doi.org/10.1109/ACCESS.2019.2916564
Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114(3), 505–518. https://doi.org/10.1016/S0165-0114(98)00244-9
Takahashi, W. (2000). Nonlinear functional analysis: Fixed point theory and its applications. Yokohama Publishers.
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539. https://doi.org/10.1002/int.20418
Wang, D., & Zhao, J. (2016). Design optimization of mechanical properties of ceramic tool material during turning of ultra-high-strength steel 300M with AHP and CRITIC method. The International Journal of Advanced Manufacturing Technology, 84(9–12), 2381–2390. https://doi.org/10.1007/s00170-015-7903-7
Wang, Y. M. (1998). Using the method of maximizing deviations to make decision for multi-idicies. System Engineering and Electronics, 20, 24–26.
Wang, Y. M., & Parkan, C. (2006). A general multiple attribute decision-making approach for integrating subjective preferences and objective information. Fuzzy Sets and Systems, 157(10), 1333–1345. https://doi.org/10.1016/j.fss.2005.11.017
Wu, J., Liu, X. D., Wang, Z. W., & Zhang, S. T. (2019). Dynamic emergency decision-making method with probabilistic hesitant fuzzy information based on GM(1,1) and TOPSIS. IEEE Access, 7(1), 7054–7066. https://doi.org/10.1109/ACCESS.2018.2890110
Wu, Z. B., Jin, B. M., & Xu, J. P. (2018). Local feedback strategy for consensus building with probabilityhesitant fuzzy preference relations. Applied Soft Computing, 67, 691–705. https://doi.org/10.1016/j.asoc.2017.06.011
Xia, M. M., & Xu, Z. S. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3), 395–407. https://doi.org/10.1016/j.ijar.2010.09.002
Xu, Z. S., & Xia, M. M. (2011a). Distance and similarity measures for hesitant fuzzy sets. Information Sciences, 181(11), 2128–2138. https://doi.org/10.1016/j.ins.2011.01.028
Xu, Z. S., & Xia, M. M. (2011b). On distance and correlation measures of hesitant fuzzy information. International Journal of Intelligent Systems, 26(5), 410–425. https://doi.org/10.1002/int.20474
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(4), 481–503. https://doi.org/10.1007/s10700-016-9257-5
Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
Yang, T., Meng, X. Z., & Zhang, H. (2019). Healthy, standardized and sustainable development – New features and trends of China’s foreign direct investment in 2018. Journal of International Economic Cooperation, 1, 12–28.
Yuan, J. H., Li, X. Y., Xu, C. B., Zhao, C. H., & Liu, Y. X. (2019). Investment risk assessment of coalfired power plants in countries along the Belt and Road initiative based on ANP-Entropy-TODIM method. Energy, 176, 623–640. https://doi.org/10.1016/j.energy.2019.04.038
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zeleny, M. (1982). Multiple criteria decision making. McGraw-Hill.
Zhang, S., Xu, Z. S., & He, Y. (2017). Operations and integrations of probabilistic hesitant fuzzy information in decision making. Information Fusion, 38, 1–11. https://doi.org/10.1016/j.inffus.2017.02.001
Zhang, X. L., & Xu, Z. S. (2014). Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. https://doi.org/10.1002/int.21676
Zhang, X. L., & Xu, Z. S. (2015). Novel distance and similarity measures on hesitant fuzzy sets with applications to clustering analysis. Journal of Intelligent & Fuzzy Systems, 28(5), 2279–2296.
Zhao, Q. H., Zhou, X., Xie, R. F., & Li, Z. C. (2011). Comparison of three weighting methods for evaluation of the HPLC fingerprints of Cortex Fraxini. Journal of Liquid Chromatography & Related Technologies, 34(17), 2008–2019. https://doi.org/10.1080/10826076.2011.582912
Zhou, F., & Chen, T. Y. (2019). A novel distance measure for Pythagorean fuzzy sets and its applications to the technique for order preference by similarity to ideal solutions. International Journal of Computational Intelligence Systems, 12(2), 955–969. https://doi.org/10.2991/ijcis.d.190820.001
Zhou, W., & Xu, Z. S. (2018). Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Transactions on Fuzzy Systems, 26(3), 1367–1378. https://doi.org/10.1109/TFUZZ.2017.2723349
Zhu, B., & Xu, Z. S. (2018). Probability-hesitant fuzzy sets and the representation of preference relations. Technological and Economic Development of Economy, 24(3), 1029–1040. https://doi.org/10.3846/20294913.2016.1266529