For qualitative decision making problems based on decision makers’ (DMs’) risk preferences and unbalanced linguistic term sets (LTSs), a new linguistic multi-attribute decision making (MADM) method is developed. Firstly, a concept of the generalized linguistic term set (GLTS) with triangular fuzzy semantic information is introduced. In order to capture and measure the DM’s risk preference, a triangular fuzzy membership function with risk preference parameters is constructed. Then, based on the expected semantic information of linguistic terms given by the DM and the distance between two triangular fuzzy numbers, a nonlinear programming model is established to obtain an optimal GLTS. An approach to linguistic MADM considering the DM’s risk preference is developed and its detailed steps are given. Finally, a numerical example and a sensitivity analysis of risk preference parameters are examined to illustrate the feasibility and effectiveness of the proposed models.
CabrerizoF.J., Al-HmouzR., MorfeqA., BalamashA.S., MartínezM.A. and Herrera-ViedmaE., Soft consensus measures in group decision making using unbalanced fuzzy linguistic information, Soft Computing21(11) (2017), 3037–3050.
2.
CabrerizoF.J., AlonsoS. and Herrera-ViedmaE., A consensus model for group decision making problems with unbalanced fuzzy linguistic information, International Journal of Information Technology and Decision Making8(1) (2009), 109–131.
3.
CabrerizoF.J., Herrera-ViedmaE. and PedryczW., A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts, European Journal of Operational Research230(3) (2013), 624–633.
4.
CabrerizoF.J., López-GijónJ., MartínezM.A., Morente-MolineraJ.A. and Herrera-ViedmaE., A fuzzy linguistic extended libqual+model to assess service quality in academic libraries, International Journal of Information Technology and Decision Making16(1) (2017), 225–244.
5.
CabrerizoF.J., Morente-MolineraJ.A., PérezI.J., López-GijónJ. and Herrera-ViedmaE., A decision support system to develop a quality management in academic digital libraries, Information Sciences323 (2015), 48–58.
6.
ChenC.T., Extension of the TOPSIS for group decision making under fuzzy environment, Fuzzy Sets and Systems114(1) (2000), 1–9.
7.
ChengC.B., Group opinion aggregation based on a grading process: A method for constructing triangular fuzzy numbers, Computers and Mathematics with Applications48(10) (2004), 1619–1632.
8.
DongY.C., LiC.C. and HerreraF., An optimization-based approach to adjusting the unbalanced linguistic preference relations to obtain a required consistency level, Information Sciences292(5) (2015), 27–38.
9.
DongY.C., LiC.C. and HerreraF., Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its uses to deal with hesitant unbalanced linguistic information, Information Sciences367-368 (2016), 259–278.
10.
DongY.C., LiC.C., XuY.F. and GuX., Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations, Group Decision and Negotiation24(2) (2015), 217–242.
11.
DongY.C., XuY.F. and YuS., Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model, IEEE Transactions on Fuzzy Systems17(6) (2009), 1366–1378.
12.
DongY.C., ZhangG.Q., HongW.C. and YuS., Linguistic computational model based on 2-tuples and intervals, IEEE Transactions on Fuzzy Systems21(6) (2013), 1006–1018.
13.
FanZ.P. and LiuY., A method for group decision-making based on multi-granularity uncertain linguistic information, Expert Systems with Applications37(5) (2010), 4000–4008.
14.
HerreraF., Herrera-ViedmaE. and MartínezL., A fuzzy linguistic methodology to deal with unbalanced linguistic term sets, IEEE Transactions on Fuzzy Systems16(2) (2008), 354–370.
15.
HerreraF. and MartínezL., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems8(6) (2000), 746–752.
16.
HuangM., QianX.H., FangS.C. and WangX.W., Winner determination for risk aversion buyers in multi-attribute reverse auction, Omega59 (2015), 184–200.
17.
JiangX.P. and WeiG.W., Some Bonferroni mean operators with 2-tuple linguistic information and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27(5) (2014), 2153–2162.
18.
JinH.P., ParkJ.M. and KwunY.C., 2-Tuple linguistic harmonic operators and their applications in group decision making, Knowledge-Based Systems44(1) (2013), 10–19.
19.
JuY.B., LiuX.Y. and YangS.H., Trapezoid fuzzy 2-tuple linguistic aggregation operators and their applications to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27(3) (2014), 1219–1232.
20.
LiC.C. and DongY.C., Unbalanced linguistic approach for venture investment evaluation with risk attitudes, Progress in Artificial Intelligence3(1) (2014), 1–13.
21.
LiC.C., DongY.C., HerreraF., Herrera-ViedmaE. and MartínezL., Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching, Information Fusion33(C) (2017), 29–40.
22.
LiuD.N., Model for evaluating the electrical power system safety with hesitant fuzzy linguistic information, Journal of Intelligent and Fuzzy Systems29(2) (2015), 725–730.
23.
LiuW., DongY.C., ChiclanaF., CabrerizoF.J. and Herrera-ViedmaE., Group decision-making based on heterogeneous preference relations with self-confidence, Fuzzy Optimization and Decision Making (2017). article in press, 10.1007/s10700-016-9254-8.
24.
LuM. and WeiG.W., Models for multiple attribute decision making with dual hesitant fuzzy uncertain linguistic information, International Journal of Knowledge-based and Intelligent Engineering Systems20(4) (2016), 217–227.
25.
PérezI.J., CabrerizoF.J. and Herrera-ViedmaE., A mobile decision support system for dynamic group decision making problems, IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans40(6) (2010), 1244–1256.
26.
RuanC.Y. and YangJ.H., Hesitant fuzzy information aggregation operators considering confidence level and priority level, Systems Engineering and Electronics38 (2016), 2324–2330.
27.
TangY., WenL.L. and WeiG.W., Approaches to multiple attribute group decision making based on the generalized Dice similarity measures with intuitionistic fuzzy information, International Journal of Knowledge-based and Intelligent Engineering Systems21(2) (2017), 85–95.
28.
WanS.P., 2-Tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision making, Knowledge-Based Systems45(3) (2013), 31–40.
29.
WangB.L., LiangJ.Y. and QianY.H., A normalized numerical scaling method for the unbalanced multi-granular linguistic sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems23(2) (2015), 221–243.
30.
WangJ.H. and HaoJ.Y., A new version of 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems14(3) (2006), 435–445.
31.
WeiG.W., Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, International Journal of Machine Learning and Cybernetics7(6) (2016), 1093–1114.
32.
WeiG.W., Picture fuzzy cross-entropy for multiple attribute decision making problems, Journal of Business Economics and Management17(4) (2016), 491–502.
33.
WeiG.W., AlsaadiF.E., HayatT. and AlsaediA., Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making, Iranian Journal of Fuzzy Systems13(4) (2016), 1–16.
34.
WeiG.W., XuX.R. and DengD.X., Interval-valued dual hesitant fuzzy linguistic geometric aggregation operators in multiple attribute decision making, International Journal of Knowledge-based and Intelligent Engineering Systems20(4) (2016), 189–196.
35.
XuJ., WanS.P. and DongJ.Y., Aggregating decision information into Atanassov’s intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making, Applied Soft Computing41(C) (2016), 331–351.
36.
XuZ.S., Study on method for triangular fuzzy number-based multi-attribute decision making with preference information on alternatives, Systems Engineering and Electronics24(8) (2002), 9–12.
37.
XuZ.S., Deviation measures of linguistic preference relations in group decision making, Omega33(3) (2005), 249–254.
38.
XuZ.S., An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information, Group Decision and Negotiation18(2) (2009), 119–145.
39.
YueZ.L., An extended TOPSIS for determining weights of decision makers with interval numbers, Knowledge-Based Systems24 (2011), 146–153.
40.
ZhangX.Y. and WangZ.J., Approaches to multiple attribute group decision making with multi-granularity linguistic term sets, International Journal of Innovative Computing, Information and Control12(1) (2016), 275–291.
41.
ZhouW. and XuZ.S., Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites, European Journal of Operational Research254(2) (2016), 610–621.
