Abstract
The present work is focused on multi-attribute group decision-making (MAGDM) problems with the uncertain 2-tuple linguistic information (ULI2-tuple) based on new aggregation operators which can capture interrelationships of attributes by a parameter vector P. To begin with, we present some new uncertain 2-tuple linguistic MM aggregation (UL2-tuple-MM) operators to handle MAGDM problems with ULI2-tuple, including the uncertain 2-tuple linguistic Muirhead mean (UL2-tuple-MM) operator, uncertain 2-tuple linguistic weighted Muirhead mean (UL2-tuple-WMM) operator. In addition, we extend UL2-tuple-WMM operator to a new aggregation operator named extended uncertain 2-tuple linguistic weighted Muirhead mean (EUL2-tuple-WMM) operators in order to handle some decision-making problems with ULI2-tuple whose attribute values are expressed in ULI2-tuple and attribute weights are also 2-tuple linguistic information. Whilst, the some properties of these new aggregation operators are obtained and some special cases are discussed. Moreover, we propose a new method to solve the MAGDM problems with ULI2-tuple. Finally, a numerical example is given to show the validity of the proposed method and the advantages of proposed method are also analysed.
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References
F. Herrera, L. Martłne, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst. 8 (2000), 746–752
F. Herrera, L. Martłne, A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making, IEEE Trans. Syst. Man Cybern. Part B Cybern. 31 (2001), 227–234
W. Li, X. Zhou, G. Guo, Hesitant fuzzy Maclaurin symmetric mean operators and their application in multiple attribute decision making, J. Comput. Anal. Appl. 20 (2016), 459–469
J. Qin, X. Liu, W. Pedrycz, Hesitant fuzzy Maclaurin symmetric mean operators and its application to multiple attribute decision making, Int. J. Fuzzy Syst. 17 (2015), 509–520
R. Rodriguez, L. Martłnez, F. Herrera, A linguistic 2-tuple multicriteria decision making model dealing with hesitant linguistic information, in 2015 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE, Istanbul, Turkey, 2015.
C. Wei, H. Lia, A multigranularity linguistic group decisionmaking method based on hesitant 2-tuple sets, Int. J. Intell. Syst. 31 (2016), 612–634
I. Beg, T. Rashi, An intuitionistic 2-tuple linguistic information model and aggregation operators, Int. J. Intell. Syst. 31 (2016), 569–592
F. Estrella, M. Espinill, F. Herrera, L. Martinez, FLINTSTONES: a fuzzy linguistic decision tools enhancement suite based on the 2-tuple linguistic model and extensions, Info. Sci. 280 (2014), 152–170
H. Liu, J. Qi, L. Mao, Z. Zhang, Personnel selection using interval 2-tuple linguistic VIKOR method, Hum. Factor Ergon. Man. 25 (2015), 370–384
X. You, J. Yo, H. Liu, L. Zhen, Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information, Expert Syst. Appl. 42 (2015), 1906–1916
H. Liu, P. L, J. You, Y. Chen, A novel approach for FMEA: combination of interval 2-tuple linguistic variables and gray relational analysis, Qual. Reliab. Eng. Int. 31 (2015), 761–772
S. Wan, G. Xu, J. Dong, Supplier selection using ANP and ELECTRE II in interval 2-tuple linguistic environment, Info. Sci. 385–386 (2017), 19–38.
G. Wei, Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information, Knowledge Info. Syst. 25 (2009), 623–634
J. Merigo, A.M. Gil-Lafuent, Induced 2-tuple linguistic generalized aggregation operators and their application in decisionmaking, Info. Sci. 236 (2013), 1–16
N. Halouani, S. Hajlaoui, H. Chabchoub, 2-tuple linguistic aggregation operators and their application in GDM problems, in: Z. Wen and T. Li (Eds.), Foundations of Intelligent Systems (ISKE2013), Springer-Verlag Berlin Heidelberg, Taipei, Taiwan, 2014, vol. 277, pp. 845–853.
Y. Ju, X. Li, A. Wang, Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making, Soft. Comput. 20 (2016), 4037–4053
J. Park, Y. Kwun, 2-Tuple linguistic harmonic operators and their applications in group decision making, Knowledge-Based Syst. 44 (2013), 10–19
G. Wei, Some harmonic aggregation operators with 2-tuple linguistic assessment information and their application to multiple attribute group decision making, Int. J. Uncertain Fuzzy. 19 (2011), 977–998
S. Wan, 2-tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision making, Knowledge-Based Syst. 45 (2013), 31–40
S. Wan, Some hybrid geometric aggregation operators with 2-tuple linguistic information and their applications to multi-attribute group decision making, Int. J. Comput. Int. Sys. 6 (2013), 750–763
C. Li, S. Zen, T. Pan, L. Zheng, A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment, J. Comput. Syst. Sci. 80 (2014), 1339–1349
G. Wei, A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information. Expert Syst. Appl. 37 (2010), 7895–7900.
G. Wei, X. Zha, Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making, Expert Syst. Appl. 39 (2012), 5881–5886
Y. Xu, H. Wan, Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment, Appl. Soft Comput. 11 (2011), 3988–3997
Q. Wu, P. W, Y. Zhou, L. Zhou, H. Chen, X. Ma, Some 2-tuple linguistic generalized power aggregation operators and their applications to multiple attribute group decision making, J. Intell. Fuzzy Syst. 29 (2015), 423–436
Y. Xu, P. Sh, J. Merigo, H. Wang, Some proportional 2-tuple geometric aggregation operators for linguistic decision making, J. Intell. Fuzzy Syst. 25 (2013), 833–843
J. Xu, Z. Wu, A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations, Comput. Ind. Eng. 64 (2013), 999–1008
I. Beg, T. Rashi, Aggregation operators of interval-valued 2-tuple linguistic information, Int. J. Intell. Syst. 29 (2014), 634–667
H. Liu, Q. Li, J. Wu, Dependent interval 2-tuple linguistic aggregation operators and their application to multiple attribute group decision making, Int. J. Uncertain Fuzzy, 22 (2014), 717–735
F. Meng, M. Zh, X. Chen, Some generalized interval-valued 2-tuple linguistic correlated aggregation operators and their application in decision making, Informatica-Lithuan. 27 (2016), 111–139
Y. Ruan, Z. Pe, Z. Gao, Linguistic interval 2-tuple power aggregation operators and their applications, Int. J. Comput. Int. Sys. 6 (2013), 381–395
J. Wang, D. Wan, H. Zhang, X. Chen, Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators, Soft Comput. 19 (2015), 389–405
H. Zhang, The multiattribute group decision making method based on aggregation operators with interval-valued 2-tuple linguistic information, Math. Comput. Model. 56 (2012), 27–35
H. Zhang, Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making, Appl. Math. Model. 37 (2013), 4269–4282
R. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Proc. Edinb. Math. Soc. 21(3) (1902), 44–162.
P. Liu, D. Li, Some Muirhead mean operators for intuitionistic fuzzy numbers and their applications to group decision making, PLoS One. 12 (2017), e0168767.
J. Qin, X. Liu, 2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection, Kybernetes. 45 (2016), 2–29
Z. Zhang, C. Guo, New operations of hesitant fuzzy linguistic term sets with applications in multi-attribute group decision making, in the 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), Istanbul, Turkey, 2015, pp. 1–8.
C. Wei, N. Zhao, X. Tang, Operators and comparisons of hesitant fuzzy linguistic term sets, IEEE Trans. Fuzzy Syst. 22 (2014), 575–585
Z. Zhang, C. Wu, Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making, J. Intell. Fuzzy Syst. 26 (2014), 2185–2202
L. Martinez, Rosa M. Rodriguez, F. Herrera, The 2-Tuple Linguistic Model Computing with Words in Decision Making, Springer, Switzerland, 2015.
Z. Zhang, C. Gu, Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations, Int. J. Syst. Sci. 47 (2015), 2572–2587
Y. Du, F. Hou, W. Zafar, Q. Yu, Y. Zhai, A novel method for multi-attribute decision making with interval-valued pythagorean fuzzy linguistic information, Int. J. Intell. Syst. 32 (2017), 1085–1112
Z. Zhang, C. Guo, L. Martłnez, Managing multigranular linguistic distribution assessments in large-scale multiattribute group decision making, IEEE Trans. Syst. Man Cybern. Syst. 47(11) (2017), 3063–3076.
W. Yu, Z. Zhang, Q. Zhong, L. Sun, Extended TODIM for multi-criteria group decision making based on unbalanced hesitant fuzzy linguistic term sets, Comput. Ind. Eng. 114 (2017), 316–328
C. Maclaurin, Asecond letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra, Philos. Trans. Roy. Soc. Lond. Ser. A. 36 (1729), 59–96
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Liu, Y., Liu, J., Qin, Y. et al. A Novel Method Based on Extended Uncertain 2-tuple Linguistic Muirhead Mean Operators to MAGDM under Uncertain 2-Tuple Linguistic Environment. Int J Comput Intell Syst 12, 498–512 (2019). https://doi.org/10.2991/ijcis.d.190315.001
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DOI: https://doi.org/10.2991/ijcis.d.190315.001