Abstract
Hesitant fuzzy linguistic preference relation (HFLPR) as a new preference relation is introduced to express the decision makers’ (DMs’) hesitant preference information for each pairwise comparison between different alternatives or criteria. In this paper, the priority vector and consistency of HFLPR are discussed based on a two-stage optimization and multiplicative consistency. Based on the original hesitant preference information, the multiplicative consistency index of an HFLPR is defined to measure the consistency level of the HFLPR. For an unacceptable multiplicative consistent HFLPR, a goal programming model, which is an integer optimization model, is developed to derive an acceptable, multiplicative, consistent HFLPR. According to probability sampling, a linguistic preference relation (LPR) with the best consistency level and an LPR with the worst consistency level with regard to an HFLPR are defined. Combining the two LPRs, a two-stage optimization framework is constructed to obtain the HFLPR’s priority vector, which considers the DM’s risk preference. A multi-stage optimization approach is proposed to solve decision-making problems by integrating the goal programming model and the two-stage optimization framework. Two real life problems are analyzed to show the feasibility of the proposed approach.
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References
Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539
Chen SM, Hong JA (2014) Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf Sci 286:63–74
Dong YC, Li CC, Herrera F (2016) Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information. Inf Sci 367-368:259–278
Lee LW, Chen SM (2015) Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators. Inf Sci 294:513–529
Wei CP, Zhao N, Tang XJ (2014) Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 22(3):575–585
Wu ZB, Xu JP (2016) Possibility Distribution-Based Approach for MAGDM With Hesitant Fuzzy Linguistic Information. IEEE Trans Cybern 46(3):694–705
Gou XJ, Xu ZS, Liao HC (2017) Hesitant fuzzy linguistic entropy and cross entropy measures and alternative queuing method for multiple criteria decision making. Inf Sci 388-389:225–246
Liao HC, Xu ZS, Zeng XJ (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142
Liao HC, Xu ZS (2015) Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making. Expert Syst Appl 42:5328–5336
Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76:127–138
Dong JY, Chen Y, Wan SP (2018) A cosine similarity based QUALIFLEX approach with hesitant fuzzy linguistic term sets for financial performance evaluation. Appl Soft Comput 69:316–329
Liao HC, Xu ZS, Zeng XJ (2015) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355
Liao HC, Yang LY, Xu ZS (2018) Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets. Appl Soft Comput 63:223–234
Wang J, Wang JQ, Zhang HY (2016) A likelihood-based TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing. Comp Indust Eng 99:287–299
Wang JQ, Wang J, Chen QH, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic terms sets. Inf Sci 280:338–351
Feng XQ, Zhang L, Wei CP (2018) The consistency measures and priority weights of hesitant fuzzy linguistic preference relations. Appl Soft Comput 65:79–90
Wang LH, Gong ZW (2017) Priority of a Hesitant Fuzzy Linguistic Preference Relation with a Normal Distribution in Meteorological Disaster Risk Assessment. Int J Env Res Pub He 14(10):1203
Liu HB, Cai JF, Jiang L (2014) On Improving the Additive Consistency of the Fuzzy Preference Relations Based on Comparative Linguistic Expressions. Int J Intell Syst 29(6):544–559
Zhu B, Xu ZS (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22(1):35–45
Wu ZB, Xu JP (2016) Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65(3):28–40
Zhang ZM, Wu C (2014) On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl-Based Syst 72:13–27
Liu HB, Xu ZS (2017) Improving the additive and multiplicative consistency of hesitant fuzzy linguistic preference relations. Int J Intell Syst 33(6):3677–3693
Li CC, Rodríguez RM, Herrera F, Martínez L, Dong YC (2018) Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index. Inf Sci 432:347–361
Wu P, Zhou LG, Chen HY, Tao ZF (2018) Additive consistency of hesitant fuzzy linguistic preference relation with a new expansion principle for hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 27(4):716–730
Rodríguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Martínez L, Torra V, Xu XJ, Xu ZS, Herrera F (2016) A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf Fusion 29:89–97
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Xu ZS (2006) Incomplete linguistic preference relations and their fusion. Inf Fusion 7:331–337
Zhang GQ, Dong YC, Xu YF (2014) Consistency and consensus measures for linguistic preference relations based on distribution assessments. Inf Fusion 17:46–55
Dong YC, Xu YF, Yu S (2009) Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Trans Fuzzy Syst 17(6):1366–1378
Zhou W, Xu ZS (2016) Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites. Eur J Oper Res 254:610–621
Zhou LG, Merigó JM, Chen HY, Liu JP (2016) The optimal group continuous logarithm compatibility measure for interval multiplicative preference. Inf Sci 328:250–269
Dong YC, Xu YF, Li HY (2008) On consistency measures of linguistic preference Relations. Eur J Oper Res 189(2):430–444
Borwein J, Lewis AS (2010) Convex analysis and nonlinear optimization: Theory and examples. Springer Science & Business Media, Berlin
Zhang ZM, Wu C (2014) Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making. J Intell Fuzzy Syst 26(5):2185–2202
Helena GW (2014) Modifications of the Hurwicz’s decision rule. Cent Eur J Oper Res 22(4):779–794
Zhang YN, Tang J, Meng FY (2018) Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations. Appl Intell. https://doi.org/10.1007/s10489-018-1292-1
Zhou LG, He YD, Chen HY, Liu JP (2014) On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA. Appl Intell 40(2):229–243
Meng FY, Tang J, Hamido F (2019) Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making. Inf Fusion 46:77–90
Acknowledgements
The work was supported by National Natural Science Foundation of China (Nos. 71771001, 71701001, 71871001, 71501002), Natural Science Foundation for Distinguished Young Scholars of Anhui Province (No. 1908085 J03), Research Funding Project of Academic and technical leaders and reserve candidates in Anhui Province (No.2018H179), Provincial Natural Science Research Project of Anhui Colleges (Nos. KJ2015A379, KJ2017A026).
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Wu, P., Zhou, L., Chen, H. et al. Multi-stage optimization model for hesitant qualitative decision making with hesitant fuzzy linguistic preference relations. Appl Intell 50, 222–240 (2020). https://doi.org/10.1007/s10489-019-01502-8
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DOI: https://doi.org/10.1007/s10489-019-01502-8