A probabilistic linguistic VIKOR method to solve MCDM problems with inconsistent criteria for different alternatives
Abstract
VIKOR is a well-defined multiple criteria decision-making (MCDM) method since it reflects different risk attitudes of decision-makers by measuring the overall performance of an alternative under all criteria as “group value” and the worst performance of the alternative under all criteria as “individual regret”, but it cannot deal with MCDM problems where the criteria of different alternatives are inconsistent (different) and the decision information is uncertain. To address these problems, we present a probabilistic linguistic VIKOR method by combining with probabilistic linguistic term sets which portrays uncertain information such as individual hesitancy and incomplete belief flexibly. In addition, we introduce the aspired and tolerable values of criteria as reference points to measure the closeness degrees of alternatives to the ideal solution. To compare group values and individual regrets of different alternatives, we develop a vector normalization method that considers the number of criteria. The robustness of the aggregation results of group values and individual regrets is improved based on the extended Borda rule, which takes into account both values and ranks of alternatives in the aggregation. A case study of personnel evaluation demonstrates the effectiveness of the proposed method for solving MCDM problems with inconsistent criteria and uncertain decision information.
Keyword : multiple criteria decision making, VIKOR, inconsistent criteria, probabilistic linguistic term set, personnel selection
How to Cite
Wu, X., Liao, H., Zavadskas, E. K., & Antuchevičienė, J. (2022). A probabilistic linguistic VIKOR method to solve MCDM problems with inconsistent criteria for different alternatives. Technological and Economic Development of Economy, 28(2), 559–580. https://doi.org/10.3846/tede.2022.16634
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Antucheviciene, J., Zavadskas, E. K., & Zakarevicius, A. (2012). Ranking redevelopment decisions of derelict buildings and analysis of ranking results. Economic Computation and Economic Cybernetics Studies and Research, 46(2), 37–62.
Anvari, A., Zulkifli, N., & Arghish, O. (2014). Application of a modified VIKOR method for decision-making problems in lean tool selection. International Journal of Advanced Manufacturing Technology, 71, 829–841. https://doi.org/10.1007/s00170-013-5520-x
Awasthi, A., Govindan, K., & Gold, S. (2018). Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based approach. International Journal of Production Economics, 195, 106–117. https://doi.org/10.1016/j.ijpe.2017.10.013
Bausys, R., & Zavadskas, E. K. (2015). Multicriteria decision making approach by VIKOR under interval neutrosophic set environment. Economic Computation and Economic Cybernetics Studies and Research, 49(4), 33–48.
Brans, J. P., & Vincke, P. (1985). A preference ranking organisation method (The PROMETHEE method for multiple criteria decision making). Management Science, 31(6), 647–656. https://doi.org/10.1287/mnsc.31.6.647
Çalı, S., & Balaman, Ş. Y. (2019). A novel outranking based multi criteria group decision making methodology integrating ELECTRE and VIKOR under intuitionistic fuzzy environment. Expert Systems with Applications, 119, 36–50. https://doi.org/10.1016/j.eswa.2018.10.039
Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making. Springer. https://doi.org/10.1007/978-3-642-46768-4
Cinelli, M., Kadziński, M., Gonzalez, M., & Słowiński, R. (2020). How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy. Omega, 96, 102261. https://doi.org/10.1016/j.omega.2020.102261
Dağdeviren, M. (2010). A hybrid multi-criteria decision-making model for personnel selection in manufacturing systems. Journal of Intelligent Manufacturing, 21(4), 451–460. https://doi.org/10.1007/s10845-008-0200-7
Doumpos, M., & Zopounidis, C. (2019). Preference disaggregation for multicriteria decision aiding: An overview and perspectives. In M. Doumpos, J. Figueira, S. Greco, & C. Zopounidis (Eds.), New perspectives in multiple criteria decision making (pp. 115–130). Springer, Cham. https://doi.org/10.1007/978-3-030-11482-4_4
Dursun, M., & Karsak, E. E. (2010). A fuzzy MCDM approach for personnel selection. Expert Systems with Applications, 37(6), 4324–4330. https://doi.org/10.1016/j.eswa.2009.11.067
Dyer, J. S., & Smith, J. E. (2021). Innovations in the science and practice of decision analysis: The role of management science. Management Science, 67(9), 5364–5378. https://doi.org/10.1287/mnsc.2020.3652
Golec, A., & Kahya, E. (2007). A fuzzy model for competency-based employee evaluation and selection. Computers & Industrial Engineering, 52(1), 143–161. https://doi.org/10.1016/j.cie.2006.11.004
Gou, X. J., Xu, Z. S., Liao, H. C., & Herrera, F. (2021). Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. Journal of the Operational Research Society, 72(12), 2611–2630. https://doi.org/10.1080/01605682.2020.1806741
Greco, S., Matarazzo, B., & Słowiński, R. (2016). Decision rule approach. In S. Greco, M. Ehrgott, & J. R. Figueira (Eds.), International series in operations research & management science: Vol. 233. Multiple criteria decision analysis: State of the art surveys (pp. 497–552). Springer-Verlag. https://doi.org/10.1007/978-1-4939-3094-4_13
Hajiagha, S. H. R., Mahdiraji, H. A., Zavadskas, E. K., & Hashemi, S. S. (2014). Fuzzy multi-objective linear programming based on compromise VIKOR method. International Journal of Information Technology & Decision Making, 13(4), 679–698. https://doi.org/10.1142/S0219622014500667
Hashemkhani Zolfani, S. H., Torkayesh, A. E., & Bazrafshan, R. (2021). Vision-based weighting system (ViWeS) in prospective MADM. Operational Research in Engineering Sciences: Theory and Applications, 4(2), 140–150. https://doi.org/10.31181/oresta20402140z
Jing, S., Niu, Z., & Chang, P. C. (2019). The application of VIKOR for the tool selection in lean management. Journal of Intelligent Manufacturing, 30, 2901–2912. https://doi.org/10.1007/s10845-015-1152-3
Keeney, R., & Raiffa, H. (1976). Decisions with multiple objectives: Preferences and value tradeoffs. Wiley.
Kilic, H. S., Demirci, A. E., & Delen, D. (2020). An integrated decision analysis methodology based on IF-DEMATEL and IF-ELECTRE for personnel selection. Decision Support Systems, 137, 113360. https://doi.org/10.1016/j.dss.2020.113360
Komazec, N., & Petrović, A. (2019). Application of the AHP-VIKOR hybrid model in media selection for informing of endangered in emergency situations. Operational Research in Engineering Sciences: Theory and Applications, 2(2), 12–23. https://oresta.rabek.org/index.php/oresta/article/view/21
Liao, H. C., & Wu, X. L. (2020). DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega, 94, 102058. https://doi.org/10.1016/j.omega.2019.04.001
Liao, H. C., Jiang, L. S., Lev, B., & Fujita, H. (2019). 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., 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, H. C., Xu, Z. S., & Zeng, X. J. (2015). Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Transactions on Fuzzy Systems, 23(5), 1343–1355. https://doi.org/10.1109/TFUZZ.2014.2360556
Lin, H. T. (2010). Personnel selection using analytic network process and fuzzy data envelopment analysis approaches. Computers & Industrial Engineering, 59(4), 937–944. https://doi.org/10.1016/j.cie.2010.09.004
Lin, M. W., Chen, Z. Y., Xu, Z. S., Gou, X. J., & Herrera, F. (2021a). Score function based on concentration degree for probabilistic linguistic term sets: An application to TOPSIS and VIKOR. Information Sciences, 551, 270–290. https://doi.org/10.1016/j.ins.2020.10.061
Lin, S.-H., Hsu, C.-C., Zhong, T., He, X., Li, J.-H., Tzeng, G.-H., & Hsieh, J.-C. (2021b). Exploring location determinants of Asia’s unique beverage shops based on a hybrid MADM model. International Journal of Strategic Property Management, 25(4), 291–315. https://doi.org/10.3846/ijspm.2021.14796
Machina, M. J., & Schmeidler, D. (1992). A more robust definition of subjective probability. Econometrica, 60(4), 745–780. https://doi.org/10.2307/2951565
Mardani, A., Zavadskas, E. K., Govindan, K., Senin, A. A., & Jusoh, A. (2016). VIKOR technique: A systematic review of the state of the art literature on methodologies and applications. Sustainability, 8(1), 37. https://doi.org/10.3390/su8010037
Opricovic, S. (1998). Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, University of Belgrade, Belgrade.
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
Ou-Yang, Y. P., Shieh, H. M., Leu, J. D., & Tzeng, G. H. (2009). A VIKOR-based multiple criteria decision method for improving information security risk. International Journal of Information Technology & Decision Making, 8(2), 267–287. https://doi.org/10.1142/S0219622009003375
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
Panja, S., Bag, S., Hao, F., & Roy, B. (2020). A smart contract system for decentralized Borda count voting. IEEE Transactions on Engineering Management, 67(4), 1323–1339. https://doi.org/10.1109/TEM.2020.2986371
Peng, J. J., Tian, C., Zhang, W. Y., Zhang, S., & Wang, J. Q. (2020). An integrated multi-criteria decision-making framework for sustainable supplier selection under picture fuzzy environment. Technological and Economic Development of Economy, 26(3), 573–598. https://doi.org/10.3846/tede.2020.12110
Roozbahani, A., Ebrahimi, E., & Banihabib, M. E. (2018). A framework for ground water management based on Bayesian Network and MCDM techniques. Water Resources Management, 32, 4985–5005. https://doi.org/10.1007/s11269-018-2118-y
Roy, B. (1968). Classement et choix en presence de points de vue multiples (La methode ELECTRE). Revue Francaise D Informatique de Recherche Operationnelle, 2(8), 57–75. https://doi.org/10.1051/ro/196802V100571
Sałabun, W., & Urbaniak, K. (2020). A new coefficient of rankings similarity in decision-making problems. In Krzhizhanovskaya, V. et al. (Eds.), Lecture Notes in Computer Science: Vol. 12138. Computational science – ICCS 2020 (pp. 632–645). Springer, Cham. https://doi.org/10.1007/978-3-030-50417-5_47
Su, L., Wang, T., Li, H. M., Chao, Y. C., & Wang, L. Y. (2020). Multi-criteria decision making for identification of unbalanced bidding. Journal of Civil Engineering and Management, 26(1), 43–52. https://doi.org/10.3846/jcem.2019.11568
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131. https://doi.org/10.1126/science.185.4157.1124
Wang, H., Xu, Z. S., & Jun, X. J. (2018). Modeling complex linguistic expressions in qualitative decision making: An overview. Knowledge-Based Systems, 144, 174–187. https://doi.org/10.1016/j.knosys.2017.12.030
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 multi-criteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Transactions on Fuzzy Systems, 26(6), 3688–3702. https://doi.org/10.1109/TFUZZ.2018.2843330
Zadeh, L. A. (1975). The concept of a linguistic variable and its applications to approximate reasoning – Part I. Information Sciences, 8(3), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zheng, J., & Lienert, J. (2018). Stakeholder interviews with two MAVT preference elicitation philosophies in a Swiss water infrastructure decision: Aggregation using SWING-weighting and disaggregation using UTA GMS. European Journal of Operational Research, 267(1), 273–287. https://doi.org/10.1016/j.ejor.2017.11.018
Antucheviciene, J., Zakarevicius, A., & Zavadskas, E. K. (2011). Measuring congruence of ranking results applying particular MCDM methods. Informatica, 22(3), 319–338. https://doi.org/10.15388/Informatica.2011.329
Antucheviciene, J., Zavadskas, E. K., & Zakarevicius, A. (2012). Ranking redevelopment decisions of derelict buildings and analysis of ranking results. Economic Computation and Economic Cybernetics Studies and Research, 46(2), 37–62.
Anvari, A., Zulkifli, N., & Arghish, O. (2014). Application of a modified VIKOR method for decision-making problems in lean tool selection. International Journal of Advanced Manufacturing Technology, 71, 829–841. https://doi.org/10.1007/s00170-013-5520-x
Awasthi, A., Govindan, K., & Gold, S. (2018). Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based approach. International Journal of Production Economics, 195, 106–117. https://doi.org/10.1016/j.ijpe.2017.10.013
Bausys, R., & Zavadskas, E. K. (2015). Multicriteria decision making approach by VIKOR under interval neutrosophic set environment. Economic Computation and Economic Cybernetics Studies and Research, 49(4), 33–48.
Brans, J. P., & Vincke, P. (1985). A preference ranking organisation method (The PROMETHEE method for multiple criteria decision making). Management Science, 31(6), 647–656. https://doi.org/10.1287/mnsc.31.6.647
Çalı, S., & Balaman, Ş. Y. (2019). A novel outranking based multi criteria group decision making methodology integrating ELECTRE and VIKOR under intuitionistic fuzzy environment. Expert Systems with Applications, 119, 36–50. https://doi.org/10.1016/j.eswa.2018.10.039
Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making. Springer. https://doi.org/10.1007/978-3-642-46768-4
Cinelli, M., Kadziński, M., Gonzalez, M., & Słowiński, R. (2020). How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy. Omega, 96, 102261. https://doi.org/10.1016/j.omega.2020.102261
Dağdeviren, M. (2010). A hybrid multi-criteria decision-making model for personnel selection in manufacturing systems. Journal of Intelligent Manufacturing, 21(4), 451–460. https://doi.org/10.1007/s10845-008-0200-7
Doumpos, M., & Zopounidis, C. (2019). Preference disaggregation for multicriteria decision aiding: An overview and perspectives. In M. Doumpos, J. Figueira, S. Greco, & C. Zopounidis (Eds.), New perspectives in multiple criteria decision making (pp. 115–130). Springer, Cham. https://doi.org/10.1007/978-3-030-11482-4_4
Dursun, M., & Karsak, E. E. (2010). A fuzzy MCDM approach for personnel selection. Expert Systems with Applications, 37(6), 4324–4330. https://doi.org/10.1016/j.eswa.2009.11.067
Dyer, J. S., & Smith, J. E. (2021). Innovations in the science and practice of decision analysis: The role of management science. Management Science, 67(9), 5364–5378. https://doi.org/10.1287/mnsc.2020.3652
Golec, A., & Kahya, E. (2007). A fuzzy model for competency-based employee evaluation and selection. Computers & Industrial Engineering, 52(1), 143–161. https://doi.org/10.1016/j.cie.2006.11.004
Gou, X. J., Xu, Z. S., Liao, H. C., & Herrera, F. (2021). Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. Journal of the Operational Research Society, 72(12), 2611–2630. https://doi.org/10.1080/01605682.2020.1806741
Greco, S., Matarazzo, B., & Słowiński, R. (2016). Decision rule approach. In S. Greco, M. Ehrgott, & J. R. Figueira (Eds.), International series in operations research & management science: Vol. 233. Multiple criteria decision analysis: State of the art surveys (pp. 497–552). Springer-Verlag. https://doi.org/10.1007/978-1-4939-3094-4_13
Hajiagha, S. H. R., Mahdiraji, H. A., Zavadskas, E. K., & Hashemi, S. S. (2014). Fuzzy multi-objective linear programming based on compromise VIKOR method. International Journal of Information Technology & Decision Making, 13(4), 679–698. https://doi.org/10.1142/S0219622014500667
Hashemkhani Zolfani, S. H., Torkayesh, A. E., & Bazrafshan, R. (2021). Vision-based weighting system (ViWeS) in prospective MADM. Operational Research in Engineering Sciences: Theory and Applications, 4(2), 140–150. https://doi.org/10.31181/oresta20402140z
Jing, S., Niu, Z., & Chang, P. C. (2019). The application of VIKOR for the tool selection in lean management. Journal of Intelligent Manufacturing, 30, 2901–2912. https://doi.org/10.1007/s10845-015-1152-3
Keeney, R., & Raiffa, H. (1976). Decisions with multiple objectives: Preferences and value tradeoffs. Wiley.
Kilic, H. S., Demirci, A. E., & Delen, D. (2020). An integrated decision analysis methodology based on IF-DEMATEL and IF-ELECTRE for personnel selection. Decision Support Systems, 137, 113360. https://doi.org/10.1016/j.dss.2020.113360
Komazec, N., & Petrović, A. (2019). Application of the AHP-VIKOR hybrid model in media selection for informing of endangered in emergency situations. Operational Research in Engineering Sciences: Theory and Applications, 2(2), 12–23. https://oresta.rabek.org/index.php/oresta/article/view/21
Liao, H. C., & Wu, X. L. (2020). DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega, 94, 102058. https://doi.org/10.1016/j.omega.2019.04.001
Liao, H. C., Jiang, L. S., Lev, B., & Fujita, H. (2019). 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., 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, H. C., Xu, Z. S., & Zeng, X. J. (2015). Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Transactions on Fuzzy Systems, 23(5), 1343–1355. https://doi.org/10.1109/TFUZZ.2014.2360556
Lin, H. T. (2010). Personnel selection using analytic network process and fuzzy data envelopment analysis approaches. Computers & Industrial Engineering, 59(4), 937–944. https://doi.org/10.1016/j.cie.2010.09.004
Lin, M. W., Chen, Z. Y., Xu, Z. S., Gou, X. J., & Herrera, F. (2021a). Score function based on concentration degree for probabilistic linguistic term sets: An application to TOPSIS and VIKOR. Information Sciences, 551, 270–290. https://doi.org/10.1016/j.ins.2020.10.061
Lin, S.-H., Hsu, C.-C., Zhong, T., He, X., Li, J.-H., Tzeng, G.-H., & Hsieh, J.-C. (2021b). Exploring location determinants of Asia’s unique beverage shops based on a hybrid MADM model. International Journal of Strategic Property Management, 25(4), 291–315. https://doi.org/10.3846/ijspm.2021.14796
Machina, M. J., & Schmeidler, D. (1992). A more robust definition of subjective probability. Econometrica, 60(4), 745–780. https://doi.org/10.2307/2951565
Mardani, A., Zavadskas, E. K., Govindan, K., Senin, A. A., & Jusoh, A. (2016). VIKOR technique: A systematic review of the state of the art literature on methodologies and applications. Sustainability, 8(1), 37. https://doi.org/10.3390/su8010037
Opricovic, S. (1998). Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, University of Belgrade, Belgrade.
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
Ou-Yang, Y. P., Shieh, H. M., Leu, J. D., & Tzeng, G. H. (2009). A VIKOR-based multiple criteria decision method for improving information security risk. International Journal of Information Technology & Decision Making, 8(2), 267–287. https://doi.org/10.1142/S0219622009003375
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
Panja, S., Bag, S., Hao, F., & Roy, B. (2020). A smart contract system for decentralized Borda count voting. IEEE Transactions on Engineering Management, 67(4), 1323–1339. https://doi.org/10.1109/TEM.2020.2986371
Peng, J. J., Tian, C., Zhang, W. Y., Zhang, S., & Wang, J. Q. (2020). An integrated multi-criteria decision-making framework for sustainable supplier selection under picture fuzzy environment. Technological and Economic Development of Economy, 26(3), 573–598. https://doi.org/10.3846/tede.2020.12110
Roozbahani, A., Ebrahimi, E., & Banihabib, M. E. (2018). A framework for ground water management based on Bayesian Network and MCDM techniques. Water Resources Management, 32, 4985–5005. https://doi.org/10.1007/s11269-018-2118-y
Roy, B. (1968). Classement et choix en presence de points de vue multiples (La methode ELECTRE). Revue Francaise D Informatique de Recherche Operationnelle, 2(8), 57–75. https://doi.org/10.1051/ro/196802V100571
Sałabun, W., & Urbaniak, K. (2020). A new coefficient of rankings similarity in decision-making problems. In Krzhizhanovskaya, V. et al. (Eds.), Lecture Notes in Computer Science: Vol. 12138. Computational science – ICCS 2020 (pp. 632–645). Springer, Cham. https://doi.org/10.1007/978-3-030-50417-5_47
Su, L., Wang, T., Li, H. M., Chao, Y. C., & Wang, L. Y. (2020). Multi-criteria decision making for identification of unbalanced bidding. Journal of Civil Engineering and Management, 26(1), 43–52. https://doi.org/10.3846/jcem.2019.11568
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131. https://doi.org/10.1126/science.185.4157.1124
Wang, H., Xu, Z. S., & Jun, X. J. (2018). Modeling complex linguistic expressions in qualitative decision making: An overview. Knowledge-Based Systems, 144, 174–187. https://doi.org/10.1016/j.knosys.2017.12.030
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 multi-criteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Transactions on Fuzzy Systems, 26(6), 3688–3702. https://doi.org/10.1109/TFUZZ.2018.2843330
Zadeh, L. A. (1975). The concept of a linguistic variable and its applications to approximate reasoning – Part I. Information Sciences, 8(3), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zheng, J., & Lienert, J. (2018). Stakeholder interviews with two MAVT preference elicitation philosophies in a Swiss water infrastructure decision: Aggregation using SWING-weighting and disaggregation using UTA GMS. European Journal of Operational Research, 267(1), 273–287. https://doi.org/10.1016/j.ejor.2017.11.018