A criterion utility conversion technique for probabilistic linguistic multiple criteria analysis in emergency management
Abstract
In multiple criteria decision making (MCDM), the even swaps method uses the relationships of criteria to make trade-offs but the burdens of experts are heavy; the linear programming technique for multidimensional analysis of preference (LINMAP) method cannot deal with the inter-dependencies among criteria but the cognitive burdens of experts are low. Taking the advantages of both these methods, this study proposes a criterion utility conversion (CUC) technique to solve probabilistic linguistic MCDM problems given that the probabilistic linguistic term set (PLTS) can reflect the psychology of experts when making evaluations. The utility conversion process is first proposed based on the marginal utilities of criteria. Then, the criterion preference ratios of experts are refined from the utility conversion process. Based on the criterion preference ratios and the operations of PLTSs, the adjusted probabilistic linguistic expected values of alternatives are calculated. The consistency and inconsistency indexes of alternatives and criteria are defined to set up the linear programming used to work out the criterion preference ratios. An illustration about the selection of emergency logistics supplier is given to validate the proposed method. The comparative analysis indicates the low cognitive burden, high stability, and strong applicability of the proposed method.
First published online 05 July 2021
Keyword : multiple criteria analysis, criterion utility conversion, probabilistic linguistic term set, emergency logistics supplier selection
How to Cite
Qin, R., Liao, H., & Jiang, L. (2021). A criterion utility conversion technique for probabilistic linguistic multiple criteria analysis in emergency management. Technological and Economic Development of Economy, 27(5), 1207-1226. https://doi.org/10.3846/tede.2021.15051
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Altun, K., & Dereli, T. (2014). Even easier multi-issue negotiation through modified Even-Swaps considering practically dominated alternatives. Computers & Industrial Engineering, 76, 307−317. https://doi.org/10.1016/j.cie.2014.08.015
Ben Abdelaziz, F., Lang, P., & Nadeau, R. (1999). Dominance and efficiency in multicriteria decision under uncertainty. Theory and Decision, 47(3), 191−211. https://doi.org/10.1023/A:1005102326115
Chen, S. X., Wang, J. Q., & Wang, T. L. (2019). Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator. Computational & Applied Mathematics, 38(2), 88. https://doi.org/10.1007/s40314-019-0839-z
Chen, T. Y. (2019). Multiple criteria group decision making using a parametric linear programming technique for multidimensional analysis of preference under uncertainty of Pythagorean fuzziness. IEEE Access, 7, 174108−174128. https://doi.org/10.1109/ACCESS.2019.2957161
Dereli, T., & Altun, K. (2012). Modified Even-Swaps: A novel, clear, rational and an easy-to-use mechanism for multi-issue negotiation. Computers & Industrial Engineering, 63(4), 1013−1029. https://doi.org/10.1016/j.cie.2012.06.013
Elahi, G., & Yu, E. (2012). Comparing alternatives for analyzing requirements trade-offs − In the absence of numerical data. Information and Software Technology, 54(6), 517−530. https://doi.org/10.1016/j.infsof.2011.10.007
Fang, R., Liao, H. C., Yang, J. B., & Xu, D. L. (2021). Generalised probabilistic linguistic evidential reasoning approach for multi-criteria decision-making under uncertainty. Journal of the Operations Research Society, 72(1), 130−144. https://doi.org/10.1080/01605682.2019.1654415
Gomes, L. F. A. M., Rangel, L. A. D., & Fernandes, P. P. (2012). Decision aiding in plastic surgery: a multicriteria analysis. Pesquisa Operacional, 32(2), 371−387. https://doi.org/10.1590/S0101-74382012005000011
Haghighi, M. H., Mousavi, S. M., & Mohagheghi, V. (2019). A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets. Applied Soft Computing, 77, 780−796. https://doi.org/10.1016/j.asoc.2019.01.048
Hamidzadeh, Z., Sattari, S., Soltanieh, M., & Vatani, A. (2020). Development of a multi-objective decision-making model to recover flare gases in a multi flare gases zone. Energy, 203, 117815. https://doi.org/10.1016/j.energy.2020.117815
Hammond, J. S., Keeney, R. L., & Raiffa, H. (1993). Even Swaps: a rational method for making tradeoffs. Harvard Business Review, 76(2), 137−138. https://www.researchgate.net/publication/13119982
Haseli, G., Sheikh, R., & Sana, S. S. (2020). Base-criterion on multi-criteria decision-making method and its applications. International Journal of Management Science and Engineering Management, 15(2), 79−88. https://doi.org/10.1080/17509653.2019.1633964
Kajanus, M., Ahola, J., Kurttila, M., & Pesonen, M. (2001). Application of even swaps for strategy selection in a rural enterprise. Management Decision, 39(5), 394−402. https://doi.org/10.1108/00251740110395688
Kashef, M., Safari, H., Maleki, M., & Cruz-Machado, V. (2018). Solving MCDM problems based on combination of PACMAN and LINMAP. Journal of Multi-Criteria Decision Analysis, 25(5−6), 169−176. https://doi.org/10.1002/mcda.1650
Lahtinen, T. J., & Hämäläinen, R. P. (2016). Path dependence and biases in the even swaps decision analysis method. European Operations Research Perspectives, 249(3), 890–898. https://doi.org/10.1016/j.ejor.2015.09.056
Lahtinen, T. J., Hämäläinen, R. P., & Jenytin, C. (2020). On preference elicitation processes which mitigate the accumulation of biases in multi-criteria decision analysis. European Journal of Operational Research, 282(1), 201−210. https://doi.org/10.1016/j.ejor.2019.09.004
Lei, F., Wei, G. W., Wu, J., Wei, C., & Guo, Y. F. (2020). QUALIFLEX method for MAGDM with probabilistic uncertain linguistic information and its application to green supplier selection. Journal of Intelligent & Fuzzy Systems, 39(5), 6819−6831. https://doi.org/10.3233/JIFS-191737
Li, D. F. (2008). Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment. Fuzzy Optimization and Decision Making, 7(1), 17−34. https://doi.org/10.1007/s10700-007-9022-x
Li, D. F., & Wan, S. P. (2014). Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection. Expert Systems with Applications, 41(6), 3047−3059. https://doi.org/10.1016/j.eswa.2013.10.036
Li, H. L., & Ma, L. C. (2008). Visualizing decision process on spheres based on the even swap concept. Decision Support Systems, 45(2), 354−367. https://doi.org/10.1016/j.dss.2008.01.004
Liao, H. C., Jiang, L. S., Lev, B., & Fujita, H. (2019a). Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method. Applied Soft Computing, 80, 450−464. https://doi.org/10.1016/j.asoc.2019.04.018
Liao, H. C., Jiang, L. S., Xu, Z. S., Xu, J. P., & Herrera, F. (2017). A linear programming method for multiple criteria decision making with probabilistic linguistic information. Information Science, 415, 341−355. https://doi.org/10.1016/j.ins.2017.06.035
Liao, H. C., Mi, X. M., & Xu, Z. S. (2020). A survey of decision-making methods with probabilistic linguistic information: Bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optimization and Decision Making, 19(1), 81−134. https://doi.org/10.1007/s10700-019-09309-5
Liao, Z. Q., Liao, H. C., Gou, X. J., Xu, Z. S., & Zavadskas, E. K. (2019b). A hesitant fuzzy linguistic choquet integral-based MULTIMOORA method for multiple criteria decision making and its application in talent selection. Economic Computation and Economic Cybernetics Studies and Research, 53(2), 113−130. https://doi.org/10.24818/18423264/53.2.19.07
Lin, M. W., Chen, Z. Y., Liao, H. C., & Xu, Z. S. (2019). ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing. Nonlinear Dynamics, 96(3), 2125–2143. https://doi.org/10.1007/s11071-019-04910-0
Lu, X. Y., Dong, J. Y., & Wan, S. P. (2020). A novel three-phase LINMAP method for hybrid multi-criteria group decision making with dual hesitant fuzzy truth degrees. IEEE Access, 8, 112462−112483. https://doi.org/10.1109/ACCESS.2020.3001941
Mehrabadi, Z. K., & Boyaghchi, F. A. (2019). Thermodynamic, economic and environmental impact studies on various distillation units integrated with gasification-based multi-generation system: comparative study and optimization. Journal of Cleaner Production, 241, 118333. https://doi.org/10.1016/j.jclepro.2019.118333
Mi, X. M., Liao, H. C., Wu, X. L., & Xu, Z. S. (2020). Probabilistic linguistic information fusion: a survey on aggregation operators in terms of principles, definitions, classifications, applications and challenges. International Journal of Intelligent Systems, 35(3), 529−556. https://doi.org/10.1002/int.22216
Milutinovic, G., Ahonen-Jonnarth, U., & Seipel, S. (2018). GISwaps: a new method for decision making in continuous choice models based on even swaps. International Journal of Decision Support Systems Technology, 10(3), 57−78. https://doi.org/10.4018/IJDSST.2018070104
Mustajoki, J., & Hämäläinen, R. P. (2005). A preference programming approach to make the even swaps method even easier. Decision Analysis, 2(2), 110−123. https://doi.org/10.1287/deca.1050.0043
Mustajoki, J., & Hämäläinen, R. P. (2007). Smart-Swaps — A decision support system for multicriteria decision analysis with the even swaps method. Decision Support Systems, 44(1), 313−325. https://doi.org/10.1016/j.dss.2007.04.004
Pang, Q., Wang, H., & Xu, Z. S. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128−143. https://doi.org/10.1016/j.ins.2016.06.021
Rodríguez, R. M., Martıńez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic terms sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109−119. https://doi.org/10.1109/TFUZZ.2011.2170076
Shaikh, A., Singh, A., Ghose, D., & Shabbiruddin. (2020). Analysis and selection of optimum material to improvise braking system in automobiles using integrated Fuzzy-COPRAS methodology. International Journal of Management Science and Engineering Management, 15(4), 265−273. https://doi.org/10.1080/17509653.2020.1772895
Sheu, J. B. (2007a). Challenges of emergency logistics management. Transportation Research Part ELogistics and Transportation Review, 43(6), 655−659. https://doi.org/10.1016/j.tre.2007.01.001
Sheu, J. B. (2007b). An emergency logistics distribution approach for quick response to urgent relief demand in disasters. Transportation Research Part E-Logistics and Transportation Review, 43(6), 687−709. https://doi.org/10.1016/j.tre.2006.04.004
Srinivasan, V., & Shocker, A. D. (1973). Linear programming techniques for multidimensional analysis of preference. Psychometrica, 38, 337−342. https://doi.org/10.1007/BF02291658
Wang, J.-C., & Chen, T.-Y. (2020). A novel Pythagorean fuzzy LINMAP-based compromising approach for multiple criteria group decision-making with preference over alternatives. International Journal of Computational Intelligence Systems, 13(1), 444−463. https://doi.org/10.2991/ijcis.d.200408.001
Wang, J.-Q., Wu, J.-T., Wang, J. H., Zhang, H.-Y., & Chen, X.-H. (2014). Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Information Sciences, 288, 55−72. https://doi.org/10.1016/j.ins.2014.07.034
Wang, L., & Xu, J. Z. (2016). Emergency logistics distribution optimization model and algorithm in disaster chain. Logistics Technology, 35(8), 115−118.
Wei, G. W., Lei, F., Lin, R., Wang, R., Wei, Y., Wu, J., & Wei, C. (2020). Algorithms for probabilistic uncertain linguistic multiple attribute group decision making based on the GRA and CRITIC method: application to location planning of electric vehicle charging stations. Economic Research-Ekonomska Istraživanja, 33(1), 828−846. https://doi.org/10.1080/1331677X.2020.1734851
Wen, Z., Liao, H. C., Ren, R. X., Bai, C. G., Zavadskas, E. K., Antucheviciene, J., & Al-Barakati, A. (2019). Cold chain logistics management of medicine with an integrated multi-criteria decisionmaking method. International Journal of Environmental Research and Public Health, 16(23), 4843. https://doi.org/10.3390/ijerph16234843
Wu, X. L., & Liao, H. C. (2019). A consensus-based probabilistic linguistic gained and lost dominance score method. European Journal of Operational Research, 272(3), 1017−1027. https://doi.org/10.1016/j.ejor.2018.07.044
Wu, X. L., Liao, H. C., Xu, Z. S., Hafezalkotob, A., & Herrera, F. (2018). Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the improved borda rule. IEEE Transactions on Fuzzy Systems, 26(6), 3688−2702. https://doi.org/10.1109/TFUZZ.2018.2843330
Yao, Q. Z. (2019). Multi-objective optimization design of spur gear based on NSGA-II and decision making. Advances in Mechanical Engineering, 11(3), 1−8. https://doi.org/10.1177/1687814018824936
Zadeh, L. A. (1975). The concept of a linguistic variable and its applications to approximate reasoningPart I. Information Sciences, 8, 199−249. https://doi.org/10.1016/0020-0255(75)90036-5
Zhang, X. L., & Xing, X. M. (2017). Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability, 9(7), 1231. https://doi.org/10.3390/su9071231
Zuo, W. J., Li, D. F., Yu, G. F., & Zhang, L. P. (2019). A large group decision-making method and its application to the evaluation of property perceived service quality. Journal of Intelligent & Fuzzy Systems, 37(1), 1513−1527. https://doi.org/10.3233/JIFS-182934
Altun, K., & Dereli, T. (2014). Even easier multi-issue negotiation through modified Even-Swaps considering practically dominated alternatives. Computers & Industrial Engineering, 76, 307−317. https://doi.org/10.1016/j.cie.2014.08.015
Ben Abdelaziz, F., Lang, P., & Nadeau, R. (1999). Dominance and efficiency in multicriteria decision under uncertainty. Theory and Decision, 47(3), 191−211. https://doi.org/10.1023/A:1005102326115
Chen, S. X., Wang, J. Q., & Wang, T. L. (2019). Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator. Computational & Applied Mathematics, 38(2), 88. https://doi.org/10.1007/s40314-019-0839-z
Chen, T. Y. (2019). Multiple criteria group decision making using a parametric linear programming technique for multidimensional analysis of preference under uncertainty of Pythagorean fuzziness. IEEE Access, 7, 174108−174128. https://doi.org/10.1109/ACCESS.2019.2957161
Dereli, T., & Altun, K. (2012). Modified Even-Swaps: A novel, clear, rational and an easy-to-use mechanism for multi-issue negotiation. Computers & Industrial Engineering, 63(4), 1013−1029. https://doi.org/10.1016/j.cie.2012.06.013
Elahi, G., & Yu, E. (2012). Comparing alternatives for analyzing requirements trade-offs − In the absence of numerical data. Information and Software Technology, 54(6), 517−530. https://doi.org/10.1016/j.infsof.2011.10.007
Fang, R., Liao, H. C., Yang, J. B., & Xu, D. L. (2021). Generalised probabilistic linguistic evidential reasoning approach for multi-criteria decision-making under uncertainty. Journal of the Operations Research Society, 72(1), 130−144. https://doi.org/10.1080/01605682.2019.1654415
Gomes, L. F. A. M., Rangel, L. A. D., & Fernandes, P. P. (2012). Decision aiding in plastic surgery: a multicriteria analysis. Pesquisa Operacional, 32(2), 371−387. https://doi.org/10.1590/S0101-74382012005000011
Haghighi, M. H., Mousavi, S. M., & Mohagheghi, V. (2019). A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets. Applied Soft Computing, 77, 780−796. https://doi.org/10.1016/j.asoc.2019.01.048
Hamidzadeh, Z., Sattari, S., Soltanieh, M., & Vatani, A. (2020). Development of a multi-objective decision-making model to recover flare gases in a multi flare gases zone. Energy, 203, 117815. https://doi.org/10.1016/j.energy.2020.117815
Hammond, J. S., Keeney, R. L., & Raiffa, H. (1993). Even Swaps: a rational method for making tradeoffs. Harvard Business Review, 76(2), 137−138. https://www.researchgate.net/publication/13119982
Haseli, G., Sheikh, R., & Sana, S. S. (2020). Base-criterion on multi-criteria decision-making method and its applications. International Journal of Management Science and Engineering Management, 15(2), 79−88. https://doi.org/10.1080/17509653.2019.1633964
Kajanus, M., Ahola, J., Kurttila, M., & Pesonen, M. (2001). Application of even swaps for strategy selection in a rural enterprise. Management Decision, 39(5), 394−402. https://doi.org/10.1108/00251740110395688
Kashef, M., Safari, H., Maleki, M., & Cruz-Machado, V. (2018). Solving MCDM problems based on combination of PACMAN and LINMAP. Journal of Multi-Criteria Decision Analysis, 25(5−6), 169−176. https://doi.org/10.1002/mcda.1650
Lahtinen, T. J., & Hämäläinen, R. P. (2016). Path dependence and biases in the even swaps decision analysis method. European Operations Research Perspectives, 249(3), 890–898. https://doi.org/10.1016/j.ejor.2015.09.056
Lahtinen, T. J., Hämäläinen, R. P., & Jenytin, C. (2020). On preference elicitation processes which mitigate the accumulation of biases in multi-criteria decision analysis. European Journal of Operational Research, 282(1), 201−210. https://doi.org/10.1016/j.ejor.2019.09.004
Lei, F., Wei, G. W., Wu, J., Wei, C., & Guo, Y. F. (2020). QUALIFLEX method for MAGDM with probabilistic uncertain linguistic information and its application to green supplier selection. Journal of Intelligent & Fuzzy Systems, 39(5), 6819−6831. https://doi.org/10.3233/JIFS-191737
Li, D. F. (2008). Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment. Fuzzy Optimization and Decision Making, 7(1), 17−34. https://doi.org/10.1007/s10700-007-9022-x
Li, D. F., & Wan, S. P. (2014). Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection. Expert Systems with Applications, 41(6), 3047−3059. https://doi.org/10.1016/j.eswa.2013.10.036
Li, H. L., & Ma, L. C. (2008). Visualizing decision process on spheres based on the even swap concept. Decision Support Systems, 45(2), 354−367. https://doi.org/10.1016/j.dss.2008.01.004
Liao, H. C., Jiang, L. S., Lev, B., & Fujita, H. (2019a). Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method. Applied Soft Computing, 80, 450−464. https://doi.org/10.1016/j.asoc.2019.04.018
Liao, H. C., Jiang, L. S., Xu, Z. S., Xu, J. P., & Herrera, F. (2017). A linear programming method for multiple criteria decision making with probabilistic linguistic information. Information Science, 415, 341−355. https://doi.org/10.1016/j.ins.2017.06.035
Liao, H. C., Mi, X. M., & Xu, Z. S. (2020). A survey of decision-making methods with probabilistic linguistic information: Bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optimization and Decision Making, 19(1), 81−134. https://doi.org/10.1007/s10700-019-09309-5
Liao, Z. Q., Liao, H. C., Gou, X. J., Xu, Z. S., & Zavadskas, E. K. (2019b). A hesitant fuzzy linguistic choquet integral-based MULTIMOORA method for multiple criteria decision making and its application in talent selection. Economic Computation and Economic Cybernetics Studies and Research, 53(2), 113−130. https://doi.org/10.24818/18423264/53.2.19.07
Lin, M. W., Chen, Z. Y., Liao, H. C., & Xu, Z. S. (2019). ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing. Nonlinear Dynamics, 96(3), 2125–2143. https://doi.org/10.1007/s11071-019-04910-0
Lu, X. Y., Dong, J. Y., & Wan, S. P. (2020). A novel three-phase LINMAP method for hybrid multi-criteria group decision making with dual hesitant fuzzy truth degrees. IEEE Access, 8, 112462−112483. https://doi.org/10.1109/ACCESS.2020.3001941
Mehrabadi, Z. K., & Boyaghchi, F. A. (2019). Thermodynamic, economic and environmental impact studies on various distillation units integrated with gasification-based multi-generation system: comparative study and optimization. Journal of Cleaner Production, 241, 118333. https://doi.org/10.1016/j.jclepro.2019.118333
Mi, X. M., Liao, H. C., Wu, X. L., & Xu, Z. S. (2020). Probabilistic linguistic information fusion: a survey on aggregation operators in terms of principles, definitions, classifications, applications and challenges. International Journal of Intelligent Systems, 35(3), 529−556. https://doi.org/10.1002/int.22216
Milutinovic, G., Ahonen-Jonnarth, U., & Seipel, S. (2018). GISwaps: a new method for decision making in continuous choice models based on even swaps. International Journal of Decision Support Systems Technology, 10(3), 57−78. https://doi.org/10.4018/IJDSST.2018070104
Mustajoki, J., & Hämäläinen, R. P. (2005). A preference programming approach to make the even swaps method even easier. Decision Analysis, 2(2), 110−123. https://doi.org/10.1287/deca.1050.0043
Mustajoki, J., & Hämäläinen, R. P. (2007). Smart-Swaps — A decision support system for multicriteria decision analysis with the even swaps method. Decision Support Systems, 44(1), 313−325. https://doi.org/10.1016/j.dss.2007.04.004
Pang, Q., Wang, H., & Xu, Z. S. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128−143. https://doi.org/10.1016/j.ins.2016.06.021
Rodríguez, R. M., Martıńez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic terms sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109−119. https://doi.org/10.1109/TFUZZ.2011.2170076
Shaikh, A., Singh, A., Ghose, D., & Shabbiruddin. (2020). Analysis and selection of optimum material to improvise braking system in automobiles using integrated Fuzzy-COPRAS methodology. International Journal of Management Science and Engineering Management, 15(4), 265−273. https://doi.org/10.1080/17509653.2020.1772895
Sheu, J. B. (2007a). Challenges of emergency logistics management. Transportation Research Part ELogistics and Transportation Review, 43(6), 655−659. https://doi.org/10.1016/j.tre.2007.01.001
Sheu, J. B. (2007b). An emergency logistics distribution approach for quick response to urgent relief demand in disasters. Transportation Research Part E-Logistics and Transportation Review, 43(6), 687−709. https://doi.org/10.1016/j.tre.2006.04.004
Srinivasan, V., & Shocker, A. D. (1973). Linear programming techniques for multidimensional analysis of preference. Psychometrica, 38, 337−342. https://doi.org/10.1007/BF02291658
Wang, J.-C., & Chen, T.-Y. (2020). A novel Pythagorean fuzzy LINMAP-based compromising approach for multiple criteria group decision-making with preference over alternatives. International Journal of Computational Intelligence Systems, 13(1), 444−463. https://doi.org/10.2991/ijcis.d.200408.001
Wang, J.-Q., Wu, J.-T., Wang, J. H., Zhang, H.-Y., & Chen, X.-H. (2014). Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Information Sciences, 288, 55−72. https://doi.org/10.1016/j.ins.2014.07.034
Wang, L., & Xu, J. Z. (2016). Emergency logistics distribution optimization model and algorithm in disaster chain. Logistics Technology, 35(8), 115−118.
Wei, G. W., Lei, F., Lin, R., Wang, R., Wei, Y., Wu, J., & Wei, C. (2020). Algorithms for probabilistic uncertain linguistic multiple attribute group decision making based on the GRA and CRITIC method: application to location planning of electric vehicle charging stations. Economic Research-Ekonomska Istraživanja, 33(1), 828−846. https://doi.org/10.1080/1331677X.2020.1734851
Wen, Z., Liao, H. C., Ren, R. X., Bai, C. G., Zavadskas, E. K., Antucheviciene, J., & Al-Barakati, A. (2019). Cold chain logistics management of medicine with an integrated multi-criteria decisionmaking method. International Journal of Environmental Research and Public Health, 16(23), 4843. https://doi.org/10.3390/ijerph16234843
Wu, X. L., & Liao, H. C. (2019). A consensus-based probabilistic linguistic gained and lost dominance score method. European Journal of Operational Research, 272(3), 1017−1027. https://doi.org/10.1016/j.ejor.2018.07.044
Wu, X. L., Liao, H. C., Xu, Z. S., Hafezalkotob, A., & Herrera, F. (2018). Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the improved borda rule. IEEE Transactions on Fuzzy Systems, 26(6), 3688−2702. https://doi.org/10.1109/TFUZZ.2018.2843330
Yao, Q. Z. (2019). Multi-objective optimization design of spur gear based on NSGA-II and decision making. Advances in Mechanical Engineering, 11(3), 1−8. https://doi.org/10.1177/1687814018824936
Zadeh, L. A. (1975). The concept of a linguistic variable and its applications to approximate reasoningPart I. Information Sciences, 8, 199−249. https://doi.org/10.1016/0020-0255(75)90036-5
Zhang, X. L., & Xing, X. M. (2017). Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability, 9(7), 1231. https://doi.org/10.3390/su9071231
Zuo, W. J., Li, D. F., Yu, G. F., & Zhang, L. P. (2019). A large group decision-making method and its application to the evaluation of property perceived service quality. Journal of Intelligent & Fuzzy Systems, 37(1), 1513−1527. https://doi.org/10.3233/JIFS-182934