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A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions

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Abstract

Probabilistic linguistic term set (PLTS) has been proposed to tackle qualitative information efficiently in the decision-making process to achieve computing with expressions, which can be regarded as an advanced process of computing with words. The PLTS plays an important role in decision making by providing a comprehensive way for representing complex linguistic information. Owning to its usefulness and efficiency, the PLTS has attracted a lot of researchers’ attention, and fruitful research achievements regarding it has been published since it was introduced in 2016. As the probabilistic linguistic theory is still in its infancy, a survey of it contributes to understanding the previous topics and the current issues, and predicting the future research directions in this area. To implement these goals, this paper is organized by bibliometric analysis, definitions, multiple criteria decision-making methods, preference relations, and applications. Twelve future research directions related to the probabilistic linguistic decision-making theory are indicated. This paper provides some insights for researchers and practitioners who have interest in complex linguistic decision making.

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References

  • Abramo, G., D’Angelo, C. A., & Solazzi, M. (2011). Are researchers that collaborate more at the international level top performers? An investigation on the Italian university system. Journal of Informetrics,5(1), 204–213.

    Google Scholar 

  • Agbodah, K., & Darko, A. P. (2019). Probabilistic linguistic aggregation operators based on Einstein t-norm and t-conorm and their application in multi-criteria group decision making. Symmetry,11, 39.

    MATH  Google Scholar 

  • Bai, C. Z., Zhang, R., Qian, L. X., & Wu, Y. N. (2017). Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowledge-Based Systems,119, 284–291.

    Google Scholar 

  • Bai, C. Z., Zhang, R., Shen, S., Huang, C. F., & Fan, X. (2018). Interval-valued probabilistic linguistic term sets in multi-criteria group decision making. International Journal of Intelligent Systems,33(6), 1301–1321.

    Google Scholar 

  • Behzadian, M., Kazemzadeh, R. B., Albadvi, A., & Aghdasi, M. (2010). PROMETHEE: A comprehensive literature review on methodologies and applications. European Journal of Operational Research,200(1), 198–215.

    MATH  Google Scholar 

  • Beuthe, M., & Scannella, G. (2001). Comparative analysis of UTA multicriteria methods. European Journal of Operational Research,130(2), 246–262.

    MATH  Google Scholar 

  • Chen, Z. S., Chin, K. S., Li, Y. L., & Yang, Y. (2016). Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making. Information Sciences,357, 61–87.

    MathSciNet  MATH  Google Scholar 

  • Cheng, X., Gu, J., & Xu, Z. S. (2018). Venture capital group decision-making with interaction under probabilistic linguistic environment. Knowledge-Based Systems,140, 82–91.

    Google Scholar 

  • Costa, C. A. B. E., Corte, J. M. D., & Vansnick, J. C. (2010). MACBETH (measuring attractiveness by a categorical based evaluation technique). Wiley Encyclopedia of Operations Research and Management Science. https://doi.org/10.1002/9780470400531.eorms0970.

    Article  Google Scholar 

  • Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: the critic method. Computers & Operations Research,22(7), 763–770.

    MATH  Google Scholar 

  • Dice, L. R. (1945). Measures of the amount of ecologic association between species. Ecology,26(3), 297–302.

    Google Scholar 

  • Dong, Y. C., Wu, Y. Z., Zhang, H. J., & Zhang, G. Q. (2015). Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions. Knowledge-Based Systems,82, 139–151.

    Google Scholar 

  • Durand, M., & Truck, I. (2018). A new proposal to deal with hesitant linguistic expressions on preference assessments. Information Fusion,41, 176–181.

    Google Scholar 

  • Eck, N. J. V., & Waltman, L. (2010). Software survey: VOSviewer, a computer program for bibliometric mapping. Scientometrics,84(2), 523–538.

    Google Scholar 

  • Ester, M., Kriegel, H.-P., Sander, J., & Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In E. Simoudis, J. Han, & U. Fayyad (Eds), Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (pp. 226–231).

  • Farhadinia, B., & Xu, Z. S. (2018). Ordered weighted hesitant fuzzy information fusion-based approach to multiple attribute decision making with probabilistic linguistic term sets. Fundamenta Informaticae,159(4), 361–383.

    MathSciNet  MATH  Google Scholar 

  • Feng, X. Q., Liu, Q., & Wei, C. P. (2019). Probabilistic linguistic QUALIFLEX approach with possibility degree comparison. Journal of Intelligent & Fuzzy Systems,36(1), 710–730.

    Google Scholar 

  • Gao, J., Xu, Z. S., Liang, Z. L., & Liao, H. C. (2019a). Expected consistency-based emergency decision-making with incomplete probabilistic linguistic preference relations. Knowledge-Based Systems, 176, 15–28.

    Google Scholar 

  • Gao, J., Xu, Z. S., Ren, P. J., & Liao, H. C. (2019b). An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. International Journal of Machine Learning and Cybernetics, 10(7), 1613–1629.

    Google Scholar 

  • Gazni, A., & Didegah, F. (2011). Investigating different types of research collaboration and citation impact: A case study of Harvard University’s publications. Scientometrics,87(2), 251–265.

    Google Scholar 

  • Ghorabaee, M. K., 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.

    Google Scholar 

  • Gomes, L. F. A. M., & Lima, M. M. P. P. (1991). TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Foundations of computing and decision sciences,16(3–4), 113–127.

    MATH  Google Scholar 

  • Gou, X. J., & Xu, Z. S. (2016). Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Information Sciences,372, 407–427.

    Google Scholar 

  • Hafezalkotob, A., Hafezalkotob, A., Liao, H. C., & Herrera, F. (2019a). An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges. Information Fusion,51, 145–177.

    Google Scholar 

  • Hafezalkotob, A., Hafezalkotob, A., Liao, H. C., & Herrera, F. (2019b). Interval MULTIMOORA method integrating interval Borda rule and interval best–worst-method-based weighting model: case study on hybrid vehicle engine selection. IEEE Transactions on Cybernetics, in press.. https://doi.org/10.1109/TCYB.2018.2889730.

    Article  Google Scholar 

  • Herrera, F., Herrera-Viedma, F., & Verdegay, J. L. (1995). A sequential selection process in group decision making with a linguistic assessment approach. Information Sciences,85, 223–239.

    MATH  Google Scholar 

  • Jaccard, P. (1912). The distribution of the flora in the alpine zone. New Phytologist,11, 37–50.

    Google Scholar 

  • Jiang, L. S., & Liao, H. C. (2019). Mixed fuzzy least absolute regression analysis with qualitative and probabilistic linguistic information. Fuzzy Sets and Systems. https://doi.org/10.1016/j.fss.2019.03.004.

    Article  Google Scholar 

  • Jin, C., Wang, H., & Xu, Z. S. (2019). Uncertain probabilistic linguistic term sets in group decision making. International Journal of Fuzzy Systems, 21(4), 1241–1258.

    MathSciNet  Google Scholar 

  • Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. IEEE International Conference on Neural Networks, Perth, Australia (pp. 1942–1948). https://doi.org/10.1109/ICNN.1995.488968.

  • Keršuliene, V., Zavadskas, E. K., & Turskis, Z. (2010). Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (SWARA). Journal of Business Economics and Management,11(2), 243–258.

    Google Scholar 

  • Kobina, A., Liang, D. C., & He, X. (2017). Probabilistic linguistic power aggregation operators for multi-criteria group decision making. Symmetry,9(12), 320. https://doi.org/10.3390/sym9120320.

    Article  Google Scholar 

  • Krishankumar, R., Ravichandran, K. S., Ahmed, M. I., Kar, S., & Tyagi, S. K. (2019). Probabilistic linguistic preference relation-based decision framework for multi-attribute group decision making. Symmetry,11, 2.

    MATH  Google Scholar 

  • Li, D. P., He, J. Q., Cheng, P. F., Wang, J. Q., & Zhang, H. Y. (2018). A novel selection model of surgical treatments for early gastric cancer patients based on heterogeneous multicriteria group decision-making. Symmetry,10(6), 223. https://doi.org/10.3390/sym10060223.

    Article  Google Scholar 

  • Li, D. Y., Liu, C. Y., & Gan, W. Y. (2009). A new cognitive model: Cloud model. Journal of Intelligent Systems,24, 357–375.

    MATH  Google Scholar 

  • Liang, D. C., Kobina, A., & Quan, W. (2018). Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. International Journal of Fuzzy Systems,20(7), 2234–2244.

    Google Scholar 

  • Liang, W. Z., Luo, S. Z., & Zhao, G. Y. (2019). Evaluation of cleaner production for gold mines employing a hybrid multi-criteria decision making approach. Sustainability,11, 146.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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 Sciences,415–416, 341–355.

    Google Scholar 

  • Liao, H. C., Tang, M., Li, Z. M., & Lev, B. (2019b). Bibliometric analysis for highly cited papers in operations research and management science from 2008 to 2017 based on Essential Science Indicators. Omega, 88, 223–236.

    Google Scholar 

  • Liao, H. C., & Wu, X. L. (2019). DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega. https://doi.org/10.1016/j.omega.2019.04.001.

    Article  Google Scholar 

  • Liao, H. C., Wu, X. L., Liang, X. D., Yang, J. B., Xu, D. L., & Herrera, F. (2018a). A continuous interval-valued linguistic ORESTE method for multi-criteria group decision making. Knowledge-Based Systems,153, 65–77.

    Google Scholar 

  • Liao, H. C., Wu, X. L., Mi, X. M., & Herrera, F. (2019c). An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule. Omega. https://doi.org/10.1016/j.omega.2019.03.010.

    Article  Google Scholar 

  • Liao, H. C., Xu, Z. S., Herrera-Viedma, E., & Herrera, F. (2018b). Hesitant fuzzy linguistic term set and its application in decision making: A state-of-the-art survey. International Journal of Fuzzy Systems,20(7), 2084–2110.

    MathSciNet  Google Scholar 

  • Liao, H. C., Xu, Z. S., & Zeng, X. J. (2014). Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Information Sciences,271, 125–142.

    MathSciNet  MATH  Google Scholar 

  • Liao, H. C., Yang, L. Y., & Xu, Z. S. (2018c). Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets. Applied Soft Computing,63, 223–234.

    Google Scholar 

  • 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.

    Google Scholar 

  • Lin, M. W., Wang, H. B., Xu, Z. S., Yao, Z. Q., & Huang, J. L. (2018a). Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets. International Journal of Intelligent Systems,33(12), 2402–2424.

    Google Scholar 

  • Lin, M. W., & Xu, Z. S. (2017). Probabilistic linguistic distance measures and their applications in multi-criteria group decision making. In: M. Collan, & J. Kacprzyk (Eds.), Soft Computing Applications for Group Decision-Making and Consensus Modeling, 411–440. https://doi.org/10.1007/978-3-319-60207-3_24.

    Google Scholar 

  • Lin, M. W., Xu, Z. S., Zhai, Y. L., & Yao, Z. Q. (2018b). Multi-attribute group decision-making under probabilistic uncertain linguistic environment. Journal of the Operational Research Society,69(2), 157–170.

    Google Scholar 

  • Liu, N. N., He, Y., & Xu, Z. S. (2019). A new approach to deal with consistency and consensus issues for hesitant fuzzy linguistic preference relations. Applied Soft Computing,76, 400–415.

    Google Scholar 

  • Liu, H. B., Jiang, L., & Xu, Z. S. (2018). Entropy measures of probabilistic linguistic term sets. International Journal of Computational Intelligence Systems,11, 45–57.

    Google Scholar 

  • Liu, P. D., & Li, Y. (2018). The PROMETHEE II method based on probabilistic linguistic information and their application to decision making. Informatica,29(2), 303–320.

    MathSciNet  Google Scholar 

  • Liu, P. D., & Li, Y. (2019). Multi-attribute decision making method based on generalized Maclaurin symmetric mean aggregation operators for probabilistic linguistic information. Computers & Industrial Engineering,131, 282–294.

    Google Scholar 

  • Liu, P. D., & Teng, F. (2018). Some Muirhead mean operators for probabilistic linguistic term sets and their applications to multiple attribute decision-making. Applied Soft Computing,68, 396–431.

    Google Scholar 

  • Liu, P. D., & Teng, F. (2019). Probabilistic linguistic TODIM method for selecting products through online product reviews. Information Sciences,485, 441–455.

    Google Scholar 

  • Liu, P. D., & You, X. L. (2017). Probabilistic linguistic TODIM approach for multiple attribute decision-making. Granular Computing,2(4), 333–342.

    MathSciNet  Google Scholar 

  • Llamazares, B. (2018). An analysis of the generalized TODIM method. European Journal of Operational Research,269(3), 1041–1049.

    MathSciNet  MATH  Google Scholar 

  • Luo, S. Z., Zhang, H. Y., Wang, J. Q., & Li, L. (2019). Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. Journal of the Operational Research Society, 70(12), 2039–2055.

    Google Scholar 

  • Ma, Z. Z., Zhu, J. J., & Chen, Y. (2019). A probabilistic linguistic group decision-making method from a reliability perspective based on evidential reasoning. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2018.2815716.

    Article  Google Scholar 

  • Mahalanobis, P. C. (1936). On the generalised distance in statistics. In: Proceedings of the National Institute of Science of India, 2, 49–55. https://www.insa.nic.in/writereaddata/UpLoadedFiles/PINSA/Vol02_1936_1_Art05.pdf.

  • Malik, M. G. A., Bashir, Z., Rashid, T., & Ali, J. (2018). Probabilistic hesitant intuitionistic linguistic term sets in multi-attribute group decision making. Symmetry,10(9), 392. https://doi.org/10.3390/sym10090392.

    Article  MATH  Google Scholar 

  • Misagh, F., & Yari, G. (2012). Interval entropy and informative distance. Entropy,14(3), 480–490.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • Paelinck, J. H. P. (1978). Qualiflex: A flexible multiple-criteria method. Economics Letters,1, 193–197.

    Google Scholar 

  • Pan, L., Ren, P. J., & Xu, Z. S. (2018). Therapeutic schedule evaluation for Brain-Metastasized non-small cell lung cancer with a probabilistic linguistic ELECTRE II Method. International Journal of Environmental Research and Public Health,15(9), 1799.

    Google Scholar 

  • Pang, Q., Wang, H., & Xu, Z. S. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences,369, 128–143.

    Google Scholar 

  • Peng, H. G., Zhang, H. Y., & Wang, J. Q. (2018). Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information. International Journal of Hospitality Management,68, 124–138.

    Google Scholar 

  • Rezaei, J. (2015). Best-worst multi-criteria decision-making method. Omega,53, 49–57.

    Google Scholar 

  • Rodriguez, A., & Laio, A. (2014). Clustering by fast search and find of density peaks. Science,344(6191), 1492–1496.

    Google Scholar 

  • Rodriguez, R. M., Martinez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems,20(1), 109–119.

    Google Scholar 

  • Roubens, M. (1982). Preference relations on actions and criteria in multicriteria decision making. European Journal of Operational Research,10(1), 51–55.

    MATH  Google Scholar 

  • Roy, B. (1968). Classement et choix en présence de points de vue multiples. Rairo,2(8), 57–75.

    Google Scholar 

  • Si, S. L., You, X. Y., Liu, H. C., & Zhang, P. (2018). DEMATEL technique: A systematic review of the state-of-the-art literature on methodologies and applications. Mathematical Problems in Engineering. https://doi.org/10.1155/2018/3696457.

    Article  Google Scholar 

  • Song, Y. M. (2018). Deriving the priority weights from probabilistic linguistic preference relation with unknown probabilities. PLoS ONE,13(12), e0208855.

    Google Scholar 

  • 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.

    Google Scholar 

  • Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology,15(1), 72–101.

    Google Scholar 

  • Srinivasan, V., & Shocker, A. D. (1973). Linear programming techniques for multidimensional analysis of preferences. Psychometrika,38(3), 337–369.

    MathSciNet  MATH  Google Scholar 

  • Tang, M., Long, Y. L., Liao, H. C., & Xu, Z. S. (2019). Inclusion measures of probabilistic linguistic term sets and their application in classifying cities in the economic zone of Chengdu plain. Applied Soft Computing, 82, 105572.

  • Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems,12, 117–131.

    MathSciNet  MATH  Google Scholar 

  • Tseng, M. L., Wu, K. J., Hu, J. Y., & Wang, C. (2018). Decision-making model for sustainable supply chain finance under uncertainties. International Journal of Production Economics,205, 30–36.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty,5(4), 297–323.

    MATH  Google Scholar 

  • Vansnick, J. C. (1986). On the problem of weights in multiple criteria decision making (the non-compensatory approach). European Journal of Operational Research,24(2), 288–294.

    MathSciNet  MATH  Google Scholar 

  • Wang, J. X. (2019). A MAGDM algorithm with multi-granular probabilistic linguistic information. Symmetry,11, 127.

    MATH  Google Scholar 

  • Wang, J., & Hao, J. (2006). A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems,14(3), 435–445.

    Google Scholar 

  • Wang, J. X., Liu, Y. Z., & Chen, X. M. (2018). A MAGDM model with multi-granular probabilistic linguistic power. In Proceeding of 5th International Conference on Information Science and Control Engineering, Zhengzhou, China. https://doi.org/10.1109/ICISCE.2018.00212.

  • Wang, X. K., Wang, J. Q., & Zhang, H. Y. (2019). Distance-based multicriteria group decision-making approach with probabilistic linguistic term sets. Expert Systems, 36(2), e12352. https://doi.org/10.1111/exsy.12352.

    Article  Google Scholar 

  • Wang, J. Q., Wu, J. T., Wang, J., 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(1), 55–72.

    MathSciNet  MATH  Google Scholar 

  • Wang, H., & Zhang, H. T. (2018). Multi-attribute group decision-making based on the evidential reasoning with different probabilistic linguistic term sets. In Proceeding of 2018 International Conference on Applied Mechanics, Mathematics, Modeling and Simulation (AMMMS 2018). https://doi.org/10.12783/dtcse/ammms2018/27258

  • Wu, J. H., & Chen, C. B. (1999). An alternative form for grey relational grades. The Journal of Grey System,1, 7–12.

    Google Scholar 

  • Wu, X. L., & Liao, H. C. (2018). An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making. Information Fusion,43, 13–26.

    Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • Wu, X. L., Liao, H. C., Xu, Z. S., Hafezalkotob, A., & Herrera, F. (2018). Probabilistic linguistic MULTIMOORA: 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.

    Google Scholar 

  • Wu, X. L., Zhang, C., Jiang, L. S., & Liao, H. C. (2019). An improved PROMETHEE method integrating conflict analysis with cognitive complex linguistic information: Case study of site selection for wind power plants. Cognitive Computation. https://doi.org/10.1007/s12559-019-09675-7.

    Article  Google Scholar 

  • Xie, W. Y., Xu, Z. S., & Ren, Z. L. (2018a). Dual probabilistic linguistic term set and its application on multi-criteria group decision making problems. In IEEE International Conference on Industrial Engineering and Engineering Management (pp. 1469–1474).

  • Xie, W. Y., Xu, Z. S., Ren, Z. L., & Wang, H. (2018b). Probabilistic linguistic analytic hierarchy process and its application on the performance assessment of Xiongan new area. International Journal of Information Technology & Decision Making,17(6), 1693–1724.

    Google Scholar 

  • Xu, X. Z. (2001). The SIR method: A superiority and inferiority ranking method for multiple criteria decision making. European Journal of Operational Research,131(3), 587–602.

    MathSciNet  MATH  Google Scholar 

  • Xu, Z. S. (2006). Incomplete linguistic preference relations and their fusion. Information Fusion,7(3), 331–337.

    Google Scholar 

  • Xu, Z. S., He, Y., & Wang, X. Z. (2018). An overview of probabilistic-based expressions for qualitative decision-making: Techniques, comparisons and developments. International Journal of Machine Learning and Cybernetics, 10(6), 1513–1528.

    Google Scholar 

  • Yang, J. B., & Xu, D. L. (2013). Evidential reasoning rule for evidence combination. Artificial Intelligence,205, 1–29.

    MathSciNet  MATH  Google Scholar 

  • Yu, X. B., Chen, H., & Ji, Z. H. (2019a). Combination of probabilistic linguistic term sets and PROMETHEE to evaluate meteorological disaster risk: Case study of southeastern China. Sustainability,11(5), 1405. https://doi.org/10.3390/su11051405.

    Article  Google Scholar 

  • Yu, W. W., Zhang, H., & Li, B. Q. (2019b). Operators and comparisons of probabilistic linguistic term sets. International Journal of Intelligent Systems, 34(7), 1476–1504.

    Google Scholar 

  • Zadeh, L. A. (1975). The concept of a linguistic variable and its applications to approximate reasoning—Part I. Information Sciences,8, 199–249.

    MATH  Google Scholar 

  • Zadeh, L. A. (2012). Computing with words. In J. Kacprzyk (Ed.) Springer.

  • Zavadskas, E. K., & Turskis, Z. (2010). A new additive ratio assessment (ARAS) method in multicriteria decision-making. Technological and Economic Development,16(2), 159–172.

    Google Scholar 

  • Zhai, Y. L., Xu, Z. S., & Liao, H. C. (2016). Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information. Applied Soft Computing,49, 801–816.

    Google Scholar 

  • Zhang, C. B., Zhang, H. Y., & Wang, J. Q. (2018b). Personalized restaurant recommendation method combining group correlations and customer preferences. Information Sciences,454–455, 128–143.

    Google Scholar 

  • Zhang, G. Q., Dong, Y. C., & Xu, Y. F. (2014). Consistency and consensus measures for linguistic preference relations based on distribution assessments. Information Fusion,17(1), 46–55.

    Google Scholar 

  • Zhang, L. (2017). The group decision making process based on probabilistic linguistic preference relations. International Journal of Science,4(8), 159–170.

    Google Scholar 

  • Zhang, P. H., & She, S. X. (2017). Assessment of service quality in wireless sensor networks with probabilistic linguistic term sets. International Journal of Online Engineering,13(3), 125–135.

    Google Scholar 

  • Zhang, X. F., Gou, X. J., Xu, Z. S., & Liao, H. C. (2019b). A projection method for multiple attribute group decision making with probabilistic linguistic term sets. International Journal of Machine Learning and Cybernetics, 10(9), 2515–2528.

    Google Scholar 

  • Zhang, X. F., Xu, Z. S., & Ren, P. J. (2019g). A novel hybrid correlation measure for probabilistic linguistic term sets and crisp numbers and its application in customer relationship management. International Journal of Information Technology & Decision Making, 18(02), 673–694.

    Google Scholar 

  • Zhang, X. L. (2018). A novel probabilistic linguistic approach for large-scale group decision making with incomplete weight information. International Journal of Fuzzy Systems,20(7), 2245–2256.

    Google Scholar 

  • Zhang, X. L., Liao, H. C., Xu, B., & Xiong, M. F. (2019a). A probabilistic linguistic-based deviation method for multi-expert qualitative decision making with aspirations. Applied Soft Computing, Technique Report.

  • Zhang, X. L., & Xing, X. M. (2017). Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability,9, 1231.

    Google Scholar 

  • Zhang, Y. X., Hao, Z. N., Xu, Z. S., & Liao, H. C. (2019c). A dynamic decision-making framework based on probabilistic linguistic Bayesian network and Prospect theory. Applied Soft Computing, Technical Report.

  • Zhang, Y. X., Hao, Z. N., Xu, Z. S., & Zeng, X. J. (2019d). A process-oriented probabilistic linguistic decision-making model with unknown attribute weights. Technical Report.

  • Zhang, Y. X., Xu, Z. S., & Liao, H. C. (2017). A consensus process for group decision making with probabilistic linguistic preference relations. Information Sciences,414, 260–275.

    Google Scholar 

  • Zhang, Y. X., Xu, Z. S., & Liao, H. C. (2018a). An ordinal consistency-based group decision making process with probabilistic linguistic preference relation. Information Sciences,467, 179–198.

    MathSciNet  Google Scholar 

  • Zhang, Y. X., Xu, Z. S., & Liao, H. C. (2019e). Water security evaluation based on the TODIM method with probabilistic linguistic term sets. Soft Computing, 23(15), 6215–6230.

    Google Scholar 

  • Zhang, Y. X., Xu, Z. S., & Liao, H. C. (2019f). A decision framework for water-human harmony evaluation based on entropy, cross entropy, and VIKOR methods with probabilistic linguistic term sets. International Journal of Fuzzy Systems, Technical Report.

  • Zhang, Y. X., Xu, Z. S., Wang, H., & Liao, H. C. (2016). Consistency-based risk assessment with probabilistic linguistic preference relation. Applied Soft Computing,49, 817–833.

    Google Scholar 

  • Zhao, M., Gao, Q., Fang, J. Y., & Xiao, Q. R. (2018). An approach to consensus measure based on possibility degrees of PLTSs in group decision making. International Journal of Fuzzy Systems,20(7), 2257–2272.

    Google Scholar 

  • Zheng, Y. H., Xu, Z. S., He, Y., & Liao, H. C. (2018). Severity assessment of chronic obstructive pulmonary disease based on hesitant fuzzy linguistic COPRAS method. Applied Soft Computing,69, 60–71.

    Google Scholar 

  • Zhu, B., Xu, Z. S., Zhang, R., & Hong, M. (2015). Generalized analytic network process. European Journal of Operational Research,244(1), 277–288.

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. 71771156, 71771155, 71971145).

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Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610064, Sichuan, China

    Huchang Liao, Xiaomei Mi & Zeshui Xu

  2. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Zeshui Xu

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  1. Huchang Liao
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  2. Xiaomei Mi
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  3. Zeshui Xu
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Correspondence to Zeshui Xu.

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Appendix

Appendix

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Liao, H., Mi, X. & Xu, Z. A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optim Decis Making 19, 81–134 (2020). https://doi.org/10.1007/s10700-019-09309-5

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