Abstract
In multiple attribute group decision making (MAGDM) processes, decision makers often use hesitant fuzzy linguistic term sets (HFLTSs) to express their opinions. However, it is incapable of representing the importance degrees or weights of different linguistic terms. The probabilistic linguistic term set (PLTS) gives each linguistic term a probability to denote their importance degree, and thus is more suitable for group decision making problems where the distribution information is available. In this paper, the PLTSs are utilized to express the experts’ assessments on each alternative with respect to each attribute in the MAGDM problem. Additionally, we establish two optimization models to derive the attribute weights. Then we propose a projection model to calculate the alternatives’ projections on both the positive and negative ideal solutions. A practical decision making problem about crossover development is given to validate the effectiveness of the projection method with PLTS information. Finally, we make some comparisons between the projection method and other existing methods, meanwhile, the advantages and limitations of the projection model are summarized.
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References
Xu ZS (2004) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168:171–184
Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119
Liao HC, Xu ZS, Zeng XJ (2015) and J.M. Merigó. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76:127–138
Pang Q, Xu ZS, Wang H (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci 369:128–143
Wang H, Xu ZS (2018) and X. J. Zeng. Modeling complex linguistic expressions in qualitative decision making: an overview. Knowl-Based Syst 144:174–187
Zhang YX, Xu ZS, Wang H (2016) and H. C. Liao. Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput 49:817–833
Bai CZ, Zhang R, Qian LX, Wu YN (2017) Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl-Based Syst 119:284–291
Zhai YL, Xu ZS, Liao HC (2016) Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information. Appl Soft Comput 49:801–816
Gou XJ, Xu ZS (2016) Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf Sci 372:407–427
Lai VS, Bo KW, Cheung W (2002) Group decision making in a multiple criteria environment: a case using the AHP in software selection. Eur J Oper Res 137(1):134–144
Roostaee SR, Izadikhah M, Lotfi FH, Rostamy-Malkhalifeh M (2012) A multi-criteria intuitionistic fuzzy group decision making method for supplier selection with VIKOR method. Int J Fuzzy Syst Appl 2(1):1–17
Gul M, Celik E, Aydin N, Gumus AT, Guneri AF (2016) A state of the art literature review of vikor and its fuzzy extensions on applications. Appl Soft Comput 46:60–89
Chen CT (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1–9
Shih HS, Shyur HJ, Lee ES (2007) An extension of TOPSIS for group decision making. Math Comput Model 45(7–8):801–813
Zheng GZ, Jing YY, Huang HX, Gao YF (2010) Application of improved grey relational projection method to evaluate sustainable building envelope performance. Appl Energy 87(2):710–720
Xu ZS, Hu H (2011) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267–280
Yue ZL (2012) Approach to group decision making based on determining the weights of experts by using projection method. Appl Math Model 36(7):2900–2910
Xu GL, Liu F (2013) An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection. Appl Math Model 37(6):3929–3943
Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Inf Sci 85(4):223–239
Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Springer-Verlag, Berlin
Xu ZS, Wang H (2017) On the syntax and semantics of virtual linguistic terms for information fusion in decision making. Inf Fusion 34:43–48
Wang YM 1998) Using the method of maximizing deviations to make decision for multi-indices, Syst Eng Electron 7(3):24–26
Shannon CE, Weaver W (1949) The mathematical theory of communication (Urbana, IL). Philos Rev 60(3):31–32
Liu PD, Zhang X (2011) Research on the supplier selection of a supply chain based on entropy weight and improved ELECTRE-III method. Int J Prod Res 49:637–646
Kildiene S, Kaklauskas A, Zavadskas EK (2011) COPRAS Based comparative analysis of the European country management capabilities within the construction sector in the time of crisis. J Bus Econ Manag 12:417–434
Saparauskas J, Zavadskas EK, Turskis Z (2011) Selection of Facade’s alternatives of commercial and public buildings based on multiple criteria. Inte J Strateg Prop Manag 15:189–203
Simanaviciene R, Liaudanskiene R, Ustinovichius L (2012) A new synthesis method of structural, technological and safety decisions (SyMAD-3). J Civ Eng Manag 18:265–276
Yang JP, Qiu WH (2005) A measure of risk and a decision-making model based on expected utility and entropy. Eur J Oper Res 164:792–799
Wang YM, Chin KS (2006) An eigenvector method for generating normalized interval and fuzzy weights. Appl Math Comput 181:1257–1275
Xu R (2000) Fuzzy least-square priority method in the analytic hierarchy process. Fuzzy Sets Syst 112:395–404
Dalkey N (1969) The Delphi method: an experimental study of group opinion. Futures 1(5):408–426
Kim SH (1999) and B. S. Ahn. Interactive group decision making procedure under incomplete information. Eur J Oper Res 116(3):498–507
Kim SH, Sang HC, Kim JK (1999) An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach. Eur J Oper Res 118(1):139–152
Lai YJ, Liu TY, Hwang CL (1994) TOPSIS for MODM. Eur J Oper Res 76(3):486–500
Doukas H, Karakosta C, Psarras J (2010) Computing with words to assess the sustainability of renewable energy options. Expert Syst Appl 37(7):5491–5497
Kuo T (2016) A modified TOPSIS with a different ranking Index, Eur J Oper Res 260:152–160
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This study was funded by the National Natural Science Foundation of China (Nos. 71571123, 71771155).
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Zhang, X., Gou, X., Xu, Z. et al. A projection method for multiple attribute group decision making with probabilistic linguistic term sets. Int. J. Mach. Learn. & Cyber. 10, 2515–2528 (2019). https://doi.org/10.1007/s13042-018-0886-6
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DOI: https://doi.org/10.1007/s13042-018-0886-6