Managing consensus by multi-stage optimization models with linguistic preference orderings and double hierarchy linguistic preferences
Abstract
Preference ordering structures are useful and popular tools to represent experts’ preferences in the decision making process. In the existing preference orderings, they lack the research on the precise relationship between any two adjacent alternatives in the preference orderings, and the decision making methods are unreasonable. To overcome these issues, this paper establishes a novel concept of linguistic preference ordering (LPO) in which the ordering of alternatives and the relationships between two adjacent alternatives should be fused well, and develops two transformation models to transform each LPO into the corresponding double hierarchy linguistic preference relation with complete consistency. Additionally, to fully respect the experts’ expression habits and provide more refined solutions to experts, this paper establishes a multi-stage consensus optimization model by considering the suggested preferences represented in both the continuous scale and the discrete scale, and develops a multi-stage interactive consensus reaching algorithm to deal with multi-expert decision making problem with LPOs. Furthermore, some numerical examples are presented to illustrate the developed methods and models. Finally, some comparative analyses between the proposed methods and models and some existing methods have been made to show the advantages of the proposed methods and models.
First published online 24 February 2020
Keyword : linguistic preference orderings, double hierarchy linguistic preference relations, consensus, multi-stage optimization models, multi-expert decision making
How to Cite
Gou, X., Xu, Z., & Zhou, W. (2020). Managing consensus by multi-stage optimization models with linguistic preference orderings and double hierarchy linguistic preferences. Technological and Economic Development of Economy, 26(3), 642-674. https://doi.org/10.3846/tede.2020.12013
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Beliakov, G., James, S. & Wilkin, T. (2017). Aggregation and consensus for preference relations based on fuzzy partial orders. Fuzzy Optimization and Decision Making, 16(4), 409–428. https://doi.org/10.1007/s10700-016-9258-4
Ben-Arieh, D., & Easton, T. (2007). Multi-criteria group consensus under linear cost opinion elasticity. Decision Support Systems, 43(3), 713–721. https://doi.org/10.1016/j.dss.2006.11.009
Chiclana, F., Herrera, F., & Herrera-Viedma, E. (1998). Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Set and Systems, 97, 33–48. https://doi.org/10.1016/S0165-0114(96)00339-9
Del Moral, M. J., Chiclana, F., Tapia, J. M., & Herrera-Viedma, E. (2018). A comparative study on consensus measures in group decision making. International Journal of Intelligent Systems, 33(8), 1624–1638. https://doi.org/10.1002/int.21954
Dombi, J. (1995). A general framework for the utility-based and outranking methods. In Fuzzy Logic and Soft Computing (pp. 202–208). World Scientific. https://doi.org/10.1142/9789812830753_0024
Dong, Y. C., Xu, Y. F., & Li, H. Y. (2008). On consistency measures of linguistic preference relations. European Journal of Operational Research, 189(2), 430–444. https://doi.org/10.1016/j.ejor.2007.06.013
Fan, Z. P., Ma, J., Jiang, Y. P., Sun, Y. H., & Ma, L. (2006). A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations. European Journal of Operational Research, 174(1), 311–321. https://doi.org/10.1016/j.ejor.2005.03.026
Fu, Z. G., & Liao, H. C. (2019). Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection. Information Fusion, 51, 271–286. https://doi.org/10.1016/j.inffus.2019.04.002
González-Pachón, J., & Romero, C. (2001). Aggregation of partial ordinal rankings: An interval goal programming approach. Computers & Operations Research, 28, 827–834. https://doi.org/10.1016/S0305-0548(00)00010-1
Gou, X. J., & Liao, H. C. (2019). About the double hierarchy linguistic term set and its extensions. ICSES Transactions on Neural and Fuzzy Computing, 2(2), 13–20.
Gou, X. J., Liao, H. C., Wang, X. X., Xu, Z. S., & Herrera, F. (2020). Consensus based on multiplicative consistent double hierarchy linguistic preferences: Venture capital in real estate market. International Journal of Strategic Property Management, 24(01), 1–23. https://doi.org/10.3846/ijspm.2019.10431
Gou, X. J., Liao, H. C., Xu, Z. S., & Herrera, F. (2017). Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures. Information Fusion, 38, 22–34. https://doi.org/10.1016/j.inffus.2017.02.008
Gou, X. J., Liao, H. C., Xu, Z. S., & Herrera, F. (2019a). Consensus model handling minority opinions and non-cooperative behaviors in large-scale group decision-making under double hierarchy linguistic preference relations (Technical report). IEEE Transactions on Cybernetics.
Gou, X. J., Liao, H. C., Xu, Z. S., Min, R., & Herrera, F. (2019b). Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: Consistency based measures, index and repairing algorithms and decision model. Information Sciences, 489, 93–112. https://doi.org/10.1016/j.ins.2019.03.037
Gou, X. J., Xu, Z. S., & Herrera, F. (2018a). Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowledge-Based Systems, 157, 20–33. https://doi.org/10.1016/j.knosys.2018.05.008
Gou, X. J., Xu, Z. S., Liao, H. C., & Herrera, F. (2018b). Multiple criteria decision making based on distance and similarity measures with double hierarchy hesitant fuzzy linguistic term sets. Computers & Industrial Engineering, 126, 516–530. https://doi.org/10.1016/j.cie.2018.10.020
He, Y., & Xu, Z. S. (2018). A consensus framework with different preference ordering structures and its applications in human resource selection. Computers & Industrial Engineering, 118, 80–88. https://doi.org/10.1016/j.cie.2018.02.022
Herrera, F., & Martínez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8, 746–752. https://doi.org/10.1109/91.890332
Herrera-Viedma, E., Herrera, F., Chiclana, F., & Luque, M. (2004). Some issues on consistency of fuzzy preference relations. European Journal of Operational Research, 154(1), 98–109. https://doi.org/10.1016/S0377-2217(02)00725-7
Herrera-Viedma, E., Martínez, L., Mata, F., & Chiclana, F. (2005). A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13(5), 644–658. https://doi.org/10.1109/TFUZZ.2005.856561
Hervés‐Beloso, C., & Cruces, H. V. (2018). Continuous preference orderings representable by utility functions. Journal of Economic Surveys, 33(1), 179–194. https://doi.org/10.1111/joes.12259
Kacprzyk, J., & Fedrizzi, M. (1988). A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research, 34(3), 316–325. https://doi.org/10.1016/0377-2217(88)90152-X
Kamis, N. H., Chiclana, F., & Levesley, J. (2018). Preference similarity network structural equivalence clustering based consensus group decision making model. Applied Soft Computing, 67, 706–720. https://doi.org/10.1016/j.asoc.2017.11.022
Kou, G., & Lin, C. (2014). A cosine maximization method for the priority vector derivation in AHP. European Journal of Operational Research, 235(1), 225–232. https://doi.org/10.1016/j.ejor.2013.10.019
Krishankumar, R., Subrajaa, L. S., Ravichandran, K. S., Kar S., & Saeid, A. B. (2019). A framework for multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic term set. International Journal of Fuzzy Systems, 21(4), 1130–1143. https://doi.org/10.1007/s40815-019-00618-w
Lan, J. B., Yang, M., Hu, M. M., & Liu, F. (2018). Multi-attribute group decision making based on hesitant fuzzy sets, topsis method and fuzzy preference relations. Technological and Economic Development of Economy, 24(6), 2295–2317. https://doi.org/10.3846/tede.2018.6768
Liang, H. M., Xiong, W., & Dong, Y. C. (2018). A prospect theory-based method for fusing the individual preference-approval structures in group decision making. Computers & Industrial Engineering, 117, 237–248. https://doi.org/10.1016/j.cie.2018.01.001
Liao, H. C., Xu, Z. S., Zeng, X. J., & Xu, D. L. (2016). An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations. Information Sciences, 329, 274–286. https://doi.org/10.1016/j.ins.2015.09.024
Liu, N. N., He, Y., & Xu, Z. S. (2019). Evaluate public-private-partnership’s Advancement using double hierarchy hesitant fuzzy linguistic PROMETHEE with subjective and objective information from stakeholder perspective. Technological and Economic Development of Economy, 25(3), 386–420. https://doi.org/10.3846/tede.2019.7588
Meng, F. Y., Tang, J., & Zhang, S. L. (2019). Interval linguistic fuzzy decision making in perspective of preference relations. Technological and Economic Development of Economy, 25(5), 998–1015. https://doi.org/10.3846/tede.2019.10548
Montserrat-Adell, J., Xu, Z. S., Gou, X. J., & Agell, N. (2019). Free double hierarchy hesitant fuzzy linguistic term sets: An application on raking alternatives in GDM. Information Fusion, 47, 45–59. https://doi.org/10.1016/j.inffus.2018.07.002
Morente-Molinera, J. A., Kou, G., Pérez, I. J., Samuylov, K., Selamat, A., & Herrera-Viedma, E. (2018). A group decision making support system for the Web: How to work in environments with a high number of participants and alternatives. Applied Soft Computing, 68, 191–201. https://doi.org/10.1016/j.asoc.2018.03.047
Morente-Molinera, J. A., Kou, G., Samuylov, K., Ureña, R., & Herrera-Viedma, E. (2019). Carrying out consensual group decision making processes under social networks using sentiment analysis over comparative expressions. Knowledge-Based Systems, 165, 335–345. https://doi.org/10.1016/j.knosys.2018.12.006
Parreiras, R., Ekel, P., & Bernardes, F. (2012). A dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling. Information Sciences, 211, 1–17. https://doi.org/10.1016/j.ins.2012.05.001
Schubert, J. (1995). On p in a decision-theoretic apparatus of Dempster-Shafer theory. International Journal of Approximate Reasoning, 13, 185–200. https://doi.org/10.1016/0888-613X(95)00061-K
Song, Y. M., & Hu, J. (2019). Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation. Applied Soft and Computing, 80, 712–722. https://doi.org/10.1016/j.asoc.2019.04.036
Song, Y. M., & Li, G. X. (2019). A large-scale group decision making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection. Journal of the Operational Research Society, 70(5), 827–841. https://doi.org/10.1080/01605682.2018.1458017
Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets Systems, 12, 117–131. https://doi.org/10.1016/0165-0114(84)90032-0
Tanino, T. (1988). Fuzzy preference relations in group decision making. In J. Kacprzyk & M. Roubens (Eds.), Non-Conventional Preference Relations in Decision Making (pp. 54–71). Springer, Berlin. https://doi.org/10.1007/978-3-642-51711-2_4
Wan, S. P., Wang, F. & Dong, J. Y. (2018). A group decision-making method considering both the group consensus and multiplicative consistency of interval-valued intuitionistic fuzzy preference relations. Information Sciences, 466, 109–128. https://doi.org/10.1016/j.ins.2018.07.031
Wu, Z. B., Huang, S., & Xu, J. P. (2019a). Multi-stage optimization models for individual consistency and group consensus with preference relations. European Journal of Operational Research, 275, 182–194. https://doi.org/10.1016/j.ejor.2018.11.014
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
Wu, H. Y., Ren, P. J., & Xu, Z. S. (2019b). Hesitant fuzzy linguistic consensus model based on trustrecommendation mechanism for hospital expert consultation. IEEE Transactions on Fuzzy Systems, 27(11), 2227–2241. https://doi.org/10.1109/TFUZZ.2019.2896836
Wu, Z. B., & Xu, J. P. (2018). A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Information Fusion, 41, 217–231. https://doi.org/10.1016/j.inffus.2017.09.011
Xu, Y. J., Wen, X. W., & Zhang, W. C. (2018). A two-stage consensus method for large-scale multiattribute group decision making with an application to earthquake shelter selection. Computers & Industrial Engineering, 116, 113–129. https://doi.org/10.1016/j.cie.2017.11.025
Xu, Y. J., Herrera, F., & Wang, H. M. (2016). A distance-based framework to deal with ordinal and additive inconsistencies for fuzzy reciprocal preference relations. Information Sciences, 328, 189–205. https://doi.org/10.1016/j.ins.2015.08.034
Xu, Z. S. (2005). Deviation measures of linguistic preference relations in group decision making. Omega, 33(3), 249–254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. (2013). Group decision making model and approach based on interval preference orderings. Computers & Industrial Engineering, 64, 797–803. https://doi.org/10.1016/j.cie.2012.12.013
Yu, D. J., & Xu, Z. S. (2020). Intuitionistic fuzzy two-sided matching model and its application to personnel-position matching problems. Journal of the Operational Research Society, 71(2), 312–321. https://doi.org/10.1080/01605682.2018.1546662
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning I. Information Sciences, 8, 199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zhang, Z. M., & Chen, S. M. (2019). A consistency and consensus-based method for group decision making with hesitant fuzzy linguistic preference relations. Information Sciences, 501, 317–336. https://doi.org/10.1016/j.ins.2019.05.086
Zhang, H. J., Dong, Y. C., Francisco, C., & Yu, S. (2019). Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design. European Journal of Operational Research, 275(2), 580–598. https://doi.org/10.1016/j.ejor.2018.11.052
Zhang, B. W., Liang, H. M., Gao, Y., & Zhang, G. Q. (2018a). The optimization-based aggregation and consensus with minimum-cost in group decision making under incomplete linguistic distribution context. Knowledge-Based Systems, 162, 92–102. https://doi.org/10.1016/j.knosys.2018.05.038
Zhang, B. W., Liang, H. M., Zhang, G. Q., & Xu, Y. F. (2018b). Minimum deviation ordinal consensus reaching in GDM with heterogeneous preference structures. Applied Soft Computing, 67, 658–676. https://doi.org/10.1016/j.asoc.2017.06.016
Zhang, Z. M., & Pedrycz, W. (2018). Goal programming approaches to managing consistency and consensus for intuitionistic multiplicative preference relations in group decision making. IEEE Transaction on Fuzzy Systems, 26(6), 3261–3275. https://doi.org/10.1109/TFUZZ.2018.2818074
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
Ben-Arieh, D., & Easton, T. (2007). Multi-criteria group consensus under linear cost opinion elasticity. Decision Support Systems, 43(3), 713–721. https://doi.org/10.1016/j.dss.2006.11.009
Chiclana, F., Herrera, F., & Herrera-Viedma, E. (1998). Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Set and Systems, 97, 33–48. https://doi.org/10.1016/S0165-0114(96)00339-9
Del Moral, M. J., Chiclana, F., Tapia, J. M., & Herrera-Viedma, E. (2018). A comparative study on consensus measures in group decision making. International Journal of Intelligent Systems, 33(8), 1624–1638. https://doi.org/10.1002/int.21954
Dombi, J. (1995). A general framework for the utility-based and outranking methods. In Fuzzy Logic and Soft Computing (pp. 202–208). World Scientific. https://doi.org/10.1142/9789812830753_0024
Dong, Y. C., Xu, Y. F., & Li, H. Y. (2008). On consistency measures of linguistic preference relations. European Journal of Operational Research, 189(2), 430–444. https://doi.org/10.1016/j.ejor.2007.06.013
Fan, Z. P., Ma, J., Jiang, Y. P., Sun, Y. H., & Ma, L. (2006). A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations. European Journal of Operational Research, 174(1), 311–321. https://doi.org/10.1016/j.ejor.2005.03.026
Fu, Z. G., & Liao, H. C. (2019). Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection. Information Fusion, 51, 271–286. https://doi.org/10.1016/j.inffus.2019.04.002
González-Pachón, J., & Romero, C. (2001). Aggregation of partial ordinal rankings: An interval goal programming approach. Computers & Operations Research, 28, 827–834. https://doi.org/10.1016/S0305-0548(00)00010-1
Gou, X. J., & Liao, H. C. (2019). About the double hierarchy linguistic term set and its extensions. ICSES Transactions on Neural and Fuzzy Computing, 2(2), 13–20.
Gou, X. J., Liao, H. C., Wang, X. X., Xu, Z. S., & Herrera, F. (2020). Consensus based on multiplicative consistent double hierarchy linguistic preferences: Venture capital in real estate market. International Journal of Strategic Property Management, 24(01), 1–23. https://doi.org/10.3846/ijspm.2019.10431
Gou, X. J., Liao, H. C., Xu, Z. S., & Herrera, F. (2017). Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures. Information Fusion, 38, 22–34. https://doi.org/10.1016/j.inffus.2017.02.008
Gou, X. J., Liao, H. C., Xu, Z. S., & Herrera, F. (2019a). Consensus model handling minority opinions and non-cooperative behaviors in large-scale group decision-making under double hierarchy linguistic preference relations (Technical report). IEEE Transactions on Cybernetics.
Gou, X. J., Liao, H. C., Xu, Z. S., Min, R., & Herrera, F. (2019b). Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: Consistency based measures, index and repairing algorithms and decision model. Information Sciences, 489, 93–112. https://doi.org/10.1016/j.ins.2019.03.037
Gou, X. J., Xu, Z. S., & Herrera, F. (2018a). Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowledge-Based Systems, 157, 20–33. https://doi.org/10.1016/j.knosys.2018.05.008
Gou, X. J., Xu, Z. S., Liao, H. C., & Herrera, F. (2018b). Multiple criteria decision making based on distance and similarity measures with double hierarchy hesitant fuzzy linguistic term sets. Computers & Industrial Engineering, 126, 516–530. https://doi.org/10.1016/j.cie.2018.10.020
He, Y., & Xu, Z. S. (2018). A consensus framework with different preference ordering structures and its applications in human resource selection. Computers & Industrial Engineering, 118, 80–88. https://doi.org/10.1016/j.cie.2018.02.022
Herrera, F., & Martínez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8, 746–752. https://doi.org/10.1109/91.890332
Herrera-Viedma, E., Herrera, F., Chiclana, F., & Luque, M. (2004). Some issues on consistency of fuzzy preference relations. European Journal of Operational Research, 154(1), 98–109. https://doi.org/10.1016/S0377-2217(02)00725-7
Herrera-Viedma, E., Martínez, L., Mata, F., & Chiclana, F. (2005). A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13(5), 644–658. https://doi.org/10.1109/TFUZZ.2005.856561
Hervés‐Beloso, C., & Cruces, H. V. (2018). Continuous preference orderings representable by utility functions. Journal of Economic Surveys, 33(1), 179–194. https://doi.org/10.1111/joes.12259
Kacprzyk, J., & Fedrizzi, M. (1988). A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research, 34(3), 316–325. https://doi.org/10.1016/0377-2217(88)90152-X
Kamis, N. H., Chiclana, F., & Levesley, J. (2018). Preference similarity network structural equivalence clustering based consensus group decision making model. Applied Soft Computing, 67, 706–720. https://doi.org/10.1016/j.asoc.2017.11.022
Kou, G., & Lin, C. (2014). A cosine maximization method for the priority vector derivation in AHP. European Journal of Operational Research, 235(1), 225–232. https://doi.org/10.1016/j.ejor.2013.10.019
Krishankumar, R., Subrajaa, L. S., Ravichandran, K. S., Kar S., & Saeid, A. B. (2019). A framework for multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic term set. International Journal of Fuzzy Systems, 21(4), 1130–1143. https://doi.org/10.1007/s40815-019-00618-w
Lan, J. B., Yang, M., Hu, M. M., & Liu, F. (2018). Multi-attribute group decision making based on hesitant fuzzy sets, topsis method and fuzzy preference relations. Technological and Economic Development of Economy, 24(6), 2295–2317. https://doi.org/10.3846/tede.2018.6768
Liang, H. M., Xiong, W., & Dong, Y. C. (2018). A prospect theory-based method for fusing the individual preference-approval structures in group decision making. Computers & Industrial Engineering, 117, 237–248. https://doi.org/10.1016/j.cie.2018.01.001
Liao, H. C., Xu, Z. S., Zeng, X. J., & Xu, D. L. (2016). An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations. Information Sciences, 329, 274–286. https://doi.org/10.1016/j.ins.2015.09.024
Liu, N. N., He, Y., & Xu, Z. S. (2019). Evaluate public-private-partnership’s Advancement using double hierarchy hesitant fuzzy linguistic PROMETHEE with subjective and objective information from stakeholder perspective. Technological and Economic Development of Economy, 25(3), 386–420. https://doi.org/10.3846/tede.2019.7588
Meng, F. Y., Tang, J., & Zhang, S. L. (2019). Interval linguistic fuzzy decision making in perspective of preference relations. Technological and Economic Development of Economy, 25(5), 998–1015. https://doi.org/10.3846/tede.2019.10548
Montserrat-Adell, J., Xu, Z. S., Gou, X. J., & Agell, N. (2019). Free double hierarchy hesitant fuzzy linguistic term sets: An application on raking alternatives in GDM. Information Fusion, 47, 45–59. https://doi.org/10.1016/j.inffus.2018.07.002
Morente-Molinera, J. A., Kou, G., Pérez, I. J., Samuylov, K., Selamat, A., & Herrera-Viedma, E. (2018). A group decision making support system for the Web: How to work in environments with a high number of participants and alternatives. Applied Soft Computing, 68, 191–201. https://doi.org/10.1016/j.asoc.2018.03.047
Morente-Molinera, J. A., Kou, G., Samuylov, K., Ureña, R., & Herrera-Viedma, E. (2019). Carrying out consensual group decision making processes under social networks using sentiment analysis over comparative expressions. Knowledge-Based Systems, 165, 335–345. https://doi.org/10.1016/j.knosys.2018.12.006
Parreiras, R., Ekel, P., & Bernardes, F. (2012). A dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling. Information Sciences, 211, 1–17. https://doi.org/10.1016/j.ins.2012.05.001
Schubert, J. (1995). On p in a decision-theoretic apparatus of Dempster-Shafer theory. International Journal of Approximate Reasoning, 13, 185–200. https://doi.org/10.1016/0888-613X(95)00061-K
Song, Y. M., & Hu, J. (2019). Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation. Applied Soft and Computing, 80, 712–722. https://doi.org/10.1016/j.asoc.2019.04.036
Song, Y. M., & Li, G. X. (2019). A large-scale group decision making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection. Journal of the Operational Research Society, 70(5), 827–841. https://doi.org/10.1080/01605682.2018.1458017
Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets Systems, 12, 117–131. https://doi.org/10.1016/0165-0114(84)90032-0
Tanino, T. (1988). Fuzzy preference relations in group decision making. In J. Kacprzyk & M. Roubens (Eds.), Non-Conventional Preference Relations in Decision Making (pp. 54–71). Springer, Berlin. https://doi.org/10.1007/978-3-642-51711-2_4
Wan, S. P., Wang, F. & Dong, J. Y. (2018). A group decision-making method considering both the group consensus and multiplicative consistency of interval-valued intuitionistic fuzzy preference relations. Information Sciences, 466, 109–128. https://doi.org/10.1016/j.ins.2018.07.031
Wu, Z. B., Huang, S., & Xu, J. P. (2019a). Multi-stage optimization models for individual consistency and group consensus with preference relations. European Journal of Operational Research, 275, 182–194. https://doi.org/10.1016/j.ejor.2018.11.014
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
Wu, H. Y., Ren, P. J., & Xu, Z. S. (2019b). Hesitant fuzzy linguistic consensus model based on trustrecommendation mechanism for hospital expert consultation. IEEE Transactions on Fuzzy Systems, 27(11), 2227–2241. https://doi.org/10.1109/TFUZZ.2019.2896836
Wu, Z. B., & Xu, J. P. (2018). A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Information Fusion, 41, 217–231. https://doi.org/10.1016/j.inffus.2017.09.011
Xu, Y. J., Wen, X. W., & Zhang, W. C. (2018). A two-stage consensus method for large-scale multiattribute group decision making with an application to earthquake shelter selection. Computers & Industrial Engineering, 116, 113–129. https://doi.org/10.1016/j.cie.2017.11.025
Xu, Y. J., Herrera, F., & Wang, H. M. (2016). A distance-based framework to deal with ordinal and additive inconsistencies for fuzzy reciprocal preference relations. Information Sciences, 328, 189–205. https://doi.org/10.1016/j.ins.2015.08.034
Xu, Z. S. (2005). Deviation measures of linguistic preference relations in group decision making. Omega, 33(3), 249–254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. (2013). Group decision making model and approach based on interval preference orderings. Computers & Industrial Engineering, 64, 797–803. https://doi.org/10.1016/j.cie.2012.12.013
Yu, D. J., & Xu, Z. S. (2020). Intuitionistic fuzzy two-sided matching model and its application to personnel-position matching problems. Journal of the Operational Research Society, 71(2), 312–321. https://doi.org/10.1080/01605682.2018.1546662
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning I. Information Sciences, 8, 199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zhang, Z. M., & Chen, S. M. (2019). A consistency and consensus-based method for group decision making with hesitant fuzzy linguistic preference relations. Information Sciences, 501, 317–336. https://doi.org/10.1016/j.ins.2019.05.086
Zhang, H. J., Dong, Y. C., Francisco, C., & Yu, S. (2019). Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design. European Journal of Operational Research, 275(2), 580–598. https://doi.org/10.1016/j.ejor.2018.11.052
Zhang, B. W., Liang, H. M., Gao, Y., & Zhang, G. Q. (2018a). The optimization-based aggregation and consensus with minimum-cost in group decision making under incomplete linguistic distribution context. Knowledge-Based Systems, 162, 92–102. https://doi.org/10.1016/j.knosys.2018.05.038
Zhang, B. W., Liang, H. M., Zhang, G. Q., & Xu, Y. F. (2018b). Minimum deviation ordinal consensus reaching in GDM with heterogeneous preference structures. Applied Soft Computing, 67, 658–676. https://doi.org/10.1016/j.asoc.2017.06.016
Zhang, Z. M., & Pedrycz, W. (2018). Goal programming approaches to managing consistency and consensus for intuitionistic multiplicative preference relations in group decision making. IEEE Transaction on Fuzzy Systems, 26(6), 3261–3275. https://doi.org/10.1109/TFUZZ.2018.2818074
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