Abstract
In some cases, decision makers (DMs) need to use multiplicative linguistic terms to express evaluations, and probabilistic linguistic preference relation (PLPR) cannot meet the needs of decision makers. Multiplicative probabilistic linguistic preference relations (MPLPRs) can solve this problem. The consistency of preference relations is crucial to ensure reliable decision results. We define the ordinal consistency of MPLPRs, and improve the ordinal consistency of MPLPRs. In order to facilitate calculation, the mapping from probabilistic linguistic term set (PLTS) to linguistic term is defined. In probabilistic linguistic information decision-making methods, some methods only collect the information of the decision matrix, and some methods only collect the information of the preference matrix, and almost no decision method that uses the decision matrix and the preference relation information at the same time, but the optimal ranking of alternatives is obtained according to the comprehensive attribute of alternatives. Based on the above considerations, first, we construct a nonlinear objective optimization model containing alternative attributes and alternative preferences. Then, a probabilistic linguistic group decision-making method based on attribute decision and multiplicative preference relations is further proposed. Finally, the feasibility of the method is illustrated by an example of hospital evaluation, and the advantages of the proposed method are verified by comparing the differences between the proposed method and other methods.
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Degani, R., Bortolan, G.: The problem of linguistic approximation in clinical decision making. Int. J. Approx. Reason. 2(2), 143–162 (1988)
Delgado, M., Verdegay, J.L., Vila, M.A.: On aggregation operations of linguistic labels. Int. J. Intell. Syst. 8(3), 351–370 (1993)
Herrera, F., Martinez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)
Bordogna, G., Fedrizzi, M., Pasi, G.: A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans. Syst. Man Cybern. A 27(1), 126–133 (1997)
Martłnez, L., Liu, J., Yang, J.B., Herrera, F.: A multigranular hierarchical linguistic model for design evaluation based on safety and cost analysis. Int. J. Intell. Syst. 20(12), 1161–1194 (2005)
Wilbik, A., Keller, J.M.: A fuzzy measure similarity between sets of linguistic summaries. IEEE Trans. Fuzzy Syst. 21(1), 183–189 (2013)
Chen, C.T., Lin, C.T., Huan, S.F.: A fuzzy approach for supplier evaluation and selection in supply chain management. Int. J. Prod. Econ. 102(2), 289–301 (2006)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-III*1. Inf. Sci. 9(1), 43–80 (1975)
Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20, 109–119 (2012)
Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision. Inf. Fusion 369, 128–143 (2016)
Gou, X.J., Xu, Z.S.: Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf. Sci. 372, 407–427 (2016)
Liu, H.B., Jiang, L., Xu, Z.S.: Entropy measures of probabilistic linguistic term sets. Int. J. Comput. Intell. Syst. 11(1), 45–57 (2018)
Lin, M.W., Xu, Z.S.: Probabilistic linguistic distance measures and their applications in multi-criteria group decision making. Soft Comput. Appl. Group Decision-making Consensus Model. 357, 411–440 (2017)
Bai, C.H., Zhang, R., Qian, L.X., Wu, Y.N.: Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl.-Based Syst. 119, 284–291 (2017)
Zhang, Y.X., Xu, Z.S., Wang, H., Liao, H.C.: A consensus process for group decision making with probabilistic preference relations. Inf. Sci. 414, 260–275 (2017)
Zhang, Y.X., Xu, Z.S., Wang, H., Liao, H.C.: An ordinal consistency-based group decision making process with probabilistic linguistic preference relation. Inf. Sci. 467, 179–198 (2018)
Liao, H.C., Jiang, L.S., Xu, Z.S., Xu, J.P., Herrera, F.: A linear programming method for multiple criteria decision making with probabilistic linguistic information. Inf. Sci. 415, 341–355 (2017)
Cheng, X., Gu, X.J.: Venture capital group decision-making with interaction under probabilistic linguistic environment. Knowl.-Based Syst. 140, 82–91 (2018)
Peng, H.G., Zhang, H.Y., Wang, J.Q.: Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information. Int. J. Hosp. Manag. 68, 124–138 (2018)
Yao, S.B., Hu, J.Q.: A minimum deviation approach for improving the consistency of uncertain 2-tuple linguistic preference relation. Comput. Ind. Eng. 117, 181–190 (2018)
Li, C.C., Rodrłguez, R.M., Martłnez, L., Dong, Y.C., Herrera, F.: Consistency of hesitant fuzzy linguistic preference relations: an interval consistency index. Inf. Sci. 432, 347–361 (2018)
Liu, H.B., Jiang, L., Xu, Z.S.: Improving the additive and multiplicative consistency of hesitant fuzzy linguistic preference relations. J. Intell. Fuzzy Syst. 33(6), 3677–3693 (2017)
Zhang, Y.X., Xu, Z.S., Wang, H., Liao, H.C.: Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput. 49, 817–833 (2016)
Luo, S.Z., Zhang, H.Y., Wang, J.Q.: Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J. Oper. Res. Soc. 12, 2039–2055 (2019)
Krishankumar, R., Ravichandran, K.S., Ahmed, M.I., Kar, S., Tyagi, S.K.: Probabilistic linguistic preference relation-based decision framework for multi-attribute group decision making. Symmetry 11(1), 2073–8994 (2019)
Song, Y.M., Li, G.X.: Consensus constructing in large-scale group decision making with multi-granular probabilistic 2-Tuple fuzzy linguistic preference relations. IEEE Access. 7, 2169–3536 (2019)
Gao, J., Xu, Z.S., Ren, P.J., Liao, H.C.: An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. Int. J. Mach. Learn. Cybern. 10(7), 1613–1629 (2019)
Gao, J., Xu, Z.S., Liang, Z.L., Liao, H.C.: Expected consistency-based emergency decision making with incomplete probabilistic linguistic preference relations. Knowl.-Based Syst. 176, 15–28 (2019)
Song, Y.M.: Deriving the priority weights from probabilistic linguistic preference relation with unknown probabilities. PLoS ONE 13(12), 1932–6203 (2018)
Song, Y.M., Hu, J.: Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation. Appl. Soft Comput. J. 80, 712–722 (2019)
Nie, R.X., Wang, J.Q.: Prospect theory-based consistency recovery strategies with multiplicative probabilistic linguistic preference relations in managing group decision making. Arab. J. Sci. Eng. 45(3), 2113–2130 (2020)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A sequential selection process in group decision making with a linguistic assessment approach. Inf. Sci. 85(4), 223–239 (1995)
Xu, Z.S.: Linguistic Decision Making: Theory and Methods. Springer, Berlin (2012)
Xu, Z.S.: EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relation. Int. J. Uncertain. Fuzz. Knowl.-Based Syst. 12(6), 791–810 (2004)
Xia, M.M., Xu, Z.S.: Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int. J. Intell. Syst. 27(9), 799–822 (2012)
Xia, M.M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52(3), 395–407 (2011)
Liao, H.C., Xu, Z.S., Zeng, X.J., Merigó, J.M.: Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl.-Based Syst. 76, 127–138 (2015)
Yang, J.J., Wang, S., Liu, C.F., Wang, R.L., Ma, J.S., Xu, K.Z., Lu, Q.H.: Power quality assessment based on combinatorial weight method of variance maximizing. J. Phys. 1087, 052042 (2018)
Zhang, K., Kong, W.R., Liu, P.P., Shi, J., Lei, Y., Zou, J.: Assessment and sequencing of air target threat based on intuitionistic fuzzy entropy and dynamic VIKOR. J. Syst. Eng. Electron. 29(2), 305–310 (2018)
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This research was supported by the National Natural Science Foundation of China (Grant No. 51878349) and Natural Science Foundation of Anhui Province of China (Grant No. 1908085MA07).
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Zhao, H., Li, B. & Li, Y. Probabilistic Linguistic Group Decision-Making Method Based on Attribute Decision and Multiplicative Preference Relations. Int. J. Fuzzy Syst. 23, 2200–2217 (2021). https://doi.org/10.1007/s40815-021-01089-8
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DOI: https://doi.org/10.1007/s40815-021-01089-8