2-tuple intuitionistic fuzzy linguistic aggregation operators in multiple attribute decision making

Document Type: Research Paper

Author

School of Business, Sichuan Normal University, Chengdu, 610101, P. R. China

Abstract

In this paper, we investigate the multiple attribute decision
making (MADM) problems with 2-tuple intuitionistic fuzzy
linguistic information. Then, we utilize arithmetic and geometric
operations to develop some 2-tuple intuitionistic fuzzy linguistic
aggregation operators. The prominent characteristic of these
proposed operators are studied. Then, we have utilized these
operators to develop some approaches to solve the 2-tuple
intuitionistic fuzzy linguistic MADM problems. Finally, a
practical example for enterprise resource planning (ERP) system
selection is given to verify the developed approach and to
demonstrate its practicality and effectiveness.

Keywords


[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets & Systems, 20(1) (1986), 87-96.
[2] K .T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets & Systems, 33(1) (1989), 37-45.
[3] I. Beg, T. Rashid, Hesitant 2-tuple linguistic information in multiple attributes group decision making, Journal of
Intelligent & Fuzzy Systems, 30(1) (2015), 143-150.
[4] F. J. Cabrerizo, J. A. Morente-Molinera, I. J. Prez, J. Lpez-Gijn, E. Herrera-Viedma, A decision support system to
develop a quality management in academic digital libraries, Information Sciences, 323 (2015), 48 - 58.
[5] K. H. Chang, T. C. Wen. A novel efficient approach for DFMEA combining 2-tuple and the OWA operator, Expert
Systems with Applications, 37(3) (2010), 2362-2370.
[6] S. Y. Chen, J. M. Tan, Handling multicriteria fuzzy decision-making problems based on vague set theory, Elsevier
North-Holland, Inc., 1994.
[7] T. Y. Chen, The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria
group decision making, Applied Soft Computing Journal, 26 (2015), 57-73.
[8] S. K. De, R. Biswas, A. R. Roy, Some operations on intuitionistic fuzzy sets, Fuzzy Sets & Systems, 114(3) (2000),
477-484.

[9] Y. C. Dong, H. V. Enrique, Consistency-driven automatic methodology to set interval numerical scales of 2-tuple
linguistic term sets and its use in the linguistic GDM with preference relation, IEEE Transactions on Cybernetics,
45(4) (2017), 780-792.
[10] Z. P. Fan, B. Feng, Y. H. Sun, W. Ou, Evaluating knowledge management capability oforganizations: A fuzzy
linguistic method, Expert Systems with Applications, 36(2) (2009), 3346-3354.
[11] Z. P. Fan, Y. Liu, A method for group decision-making based on multi-granularity uncertain linguistic information,
Pergamon Press, Inc., 2010.
[12] H. Gao, M. Lu, G. W. Wei, Y. Wei, Some novel pythagorean fuzzy interaction aggregation operators in multiple
attribute decision making, Fundamenta Informaticae, 159(4) (2017), 385-428.
[13] H. Gao, G. W. Wei, Y. Huang, Dual hesitant bipolar fuzzy hamacher prioritized aggregation operators in multiple
attribute decision making, IEEE Access, 6 (2018), 11508-11522.
[14] F. Herrera, E. Herrera-Viedma, Choice functions and mechanisms for linguistic preference relations, European
Journal of Operational Research, 120(1) (2000), 144-161.
[15] F. Herrera, E. Herrera-Viedma, Linguistic decision analysis: steps for solving decision problems under linguistic
information, Fuzzy Sets & Systems, 115(1)(2000), 67-82.
[16] F. Herrera, E. Herrera-Viedma, L. Martinez, A fuzzy linguistic methodology to deal with unbalanced linguistic term
sets, IEEE Transactions on Fuzzy Systems, 16(2) (2008), 354-370.
[17] F. Herrera, L. Martinez, The 2-tuple linguistic computational model. Advantages of its linguistic description, accu-
racy and consistency, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(1) (2001),
33-48.
[18] F. Herrera, L. Martinez, A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic
contexts in multi-expert decision-making, IEEE Transactions on Systems Man & Cybernetics Part B Cybernetics A
Publication of the IEEE Systems Man & Cybernetics Society, 1(2) (2001), 227-34.
[19] E. Herrera-Viedma, L. Martinez, F. Mata, F. Chiclana, A consensus support system model for group decision-
making problems with multigranular linguistic preference relations, IEEE Transactions on Fuzzy Systems, 13(5)
(2005), 644-658.
[20] F. Herreraab, Managing non-homogeneous information in group decision making, European Journal of Operational
Research, 166(1) (2005), 115-132.
[21] D. H. Hong, C. H. Choi, Multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets &
Systems, 114(1) (2000), 103-113.
[22] X. P. Jiang, G. W. Wei. Some bonferroni mean operators with 2-tuple linguistic information and their application
to multiple attribute decision making, Journal of Intelligent & Fuzzy Systems, 27(5) (2014), 2153-2162.
[23] C. C. Li, Y. C. Dong, F. Herrera, E. Herrera-Viedma, L. Martnez, Personalized individual semantics in computing
with words for supporting linguistic group decision making. An application on consensus reaching, Information
Fusion, 33 (2017), 29-40.
[24] D. F. Li, The GOWA operator based approach to multi-attribute decision making using intuitionistic fuzzy sets,
Mathematical & Computer Modelling, 53(5-6) (2011),1182-1196.
[25] X. W. Liao, B. Lu Y. Li, A model for selecting an ERP system based on linguistic information processing, Information
Systems, 32(7) (2007), 1005-1017.
[26] R. Lin, X. Zhao, G. W. Wei, Fuzzy number intuitionistic fuzzy prioritized operators and their application to multiple
attribute decision making, Journal of Intelligent & Fuzzy Systems, 24(4) (2013), 879-888.
[27] H. C. Liu, Q. L. Lin, J. Wu. Dependent interval 2-tuple linguistic aggregation operators and their application to
multiple attribute group decision making, International Journal of Uncertainty, Fuzziness and Knowledge-Based
Systems, 22(5) (2014), 717-735.

[28] M. Lu, G. W. Wei, Models for multiple attribute decision making with dual hesitant fuzzy uncertain linguistic
information, International Journal of Knowledge-based and Intelligent Engineering Systems, 20(4) (2016), 217-227.
[29] J. M. Merigo, M. Casanovas, L. Martinez, Linguistic aggregation operators for linguistic decision making based
on the dempster-shafer theory of evidence, International Journal of Uncertainty, Fuzziness and Knowledge-Based
Systems, 18(3) (2010), 287-304.
[30] J. A. Morente-Molinera, I. J. Prez, M. R. Urena, E. Herrera-Viedma, On multi-granular fuzzy linguistic modeling
in group decision making problems: A systematic review and future trends, Knowledge-Based Systems, 74(1) (2015),
49-60.
[31] J. D. Qin, X. W. Liu, 2-tuple linguistic muirhead mean operators for multiple attribute group decision making and
its application to supplier selection, Kybernetes, 45(1) (2016), 2-29.
[32] G. Sirbiladze, O. Badagadze, Intuitionistic fuzzy probabilistic aggregation operators based on the choquet integral:
Application in multicriteria decision-making, International Journal of Information Technology & Decision Making,
16(1) (2017), 245-279.
[33] W. S. Tai, C. T. Chen, A new evaluation model for intellectual capital based on computing with linguistic variable,
Expert Systems with Applications, 36(2) (2009), 3483-3488.
[34] X. Y. Tang, G. W. Wei, Models for green supplier selection in green supply chain management with pythagorean
2-tuple linguistic information, IEEE Access, 6 (2018), 18042-18060.
[35] B. Vahdani, S. M. Mousavi, R. Tavakkoli-Moghaddam, H. Hashemi, A new design of the elimination and choice
translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment, Applied
Mathematical Modelling, 37(4) (2013), 1781-1799.
[36] J. Wang, G. W. Wei, Y. Wei. Models for green supplier selection with some 2-tuple linguistic neutrosophic number
bonferroni mean operators, Symmetry, 10(5) (2018), 131.
[37] J. Q. Wang, D. D. Wang, H. Y. Zhang, and X. H. Chen. Multi-criteria group decision making method based on
interval 2-tuple linguistic information and choquet integral aggregation operators, Soft Computing, 19(2) (2015),
389-405.
[38] W. P. Wang, Evaluating new product development performance by fuzzy linguistic computing, Expert Systems with
Applications, 36(6) (2009), 9759-9766.
[39] G. W. Wei, Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting,
Knowledge-Based Systems, 21(8) (2008), 833-836.
[40] G. W. Wei, Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with
incomplete weight information, Knowledge & Information Systems, 25(3) (2010), 623-634.
[41] G. W. Wei, GRA method for multiple attribute decision making with incomplete weight information in intuitionistic
fuzzy setting, Knowledge-Based Systems, 23(3) (2010), 243-247.
[42] G. W.Wei, Some induced geometric aggregation operators with intuitionistic fuzzy information and their application
to group decision making, Applied Soft Computing, 10(2) (2010), 423-431.
[43] G. W.Wei, Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making, Expert
Systems with Applications, 38(9) (2011), 11671-11677.
[44] G. W. Wei, Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision
making, International Journal of Machine Learning & Cybernetics, 7(6) (2016), 1093-1114.
[45] G. W. Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems, Journal of Business Economics
& Management, 17(4) (2016), 491-502.
[46] G. W.Wei, Picture fuzzy hamacher aggregation operators and their application to multiple attribute decision making,
Fundamenta Informaticae, 157(3) (2016), 271-320.

[47] G. W. Wei, Picture uncertain linguistic bonferroni mean operators and their application to multiple attribute
decision making, Kybernetes, 46(10) (2017), 1777-1800.
[48] G. W. Wei, Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision
making, Informatica (Netherlands), 28 (2017), 547-564.
[49] G. W.Wei, Some similarity measures for picture fuzzy sets and their applications, Iranian Journal of Fuzzy Systems,
15(1) (2018), 77-89.
[50] G. W. Wei, F. E. Alsaadi, T. Hayat, A. Alsaedi, Projection models for multiple attribute decision making with
picture fuzzy information, International Journal of Machine Learning & Cybernetics, 9(4) (2018), 713-719.
[51] G. W. Wei, M. Lu, Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making,
International Journal of Intelligent Systems, 33(6) (2017), 1043-1070.
[52] G. W. Wei, M. Lu, X. Y. Tang, Y. Wei, Pythagorean hesitant fuzzy hamacher aggregation operators and their
application to multiple attribute decision making, International Journal of Intelligent Systems, 33(6) (2018), 1197-
1233.
[53] G. W.Wei, Y.Wei, Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications,
International Journal of Intelligent Systems, 33(3) (2018), 634-652.
[54] G. W. Wei, X. R. Xu, D. X. Deng, Interval-valued dual hesitant fuzzy linguistic geometric aggregation operators in
multiple attribute decision making, Journal of Intelligent & Fuzzy Systems, 33(4) (2017), 1-13.
[55] G.W. Wei, C. Wei, H. Gao, Multiple attribute decision making with interval-valued bipolar fuzzy information and
their application to emerging technology commercialization evaluation, IEEE Access, 6 (2018), 60930-60955.
[56] Y. J. Xu, F. Ma, F. F. Tao, H. M. Wang, Some methods to deal with unacceptable incomplete 2-tuple fuzzy linguistic
preference relations in group decision making, Knowledge-Based Systems, 56(3) (2014), 179-190.
[57] Z. S. Xu, A method based on linguistic aggregation operators for group decision making with linguistic preference
relations, Information Sciences, 166(1) (2004), 19-30.
[58] Z. S. Xu, A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision making
with linguistic information, Group Decision & Negotiation, 15(6) (2006), 593-604.
[59] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems, 14(6) (2018), 1179-1187.
[60] Z. S. Xu, Q. L. Da, An overview of operators for aggregating information, International Journal of Intelligent
Systems, 18(9) (2010), 953-969.
[61] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions
on Systems, Man and Cybernetics, 18(1) (1988), 183-190.
[62] R. R. Yager, Generalized OWA aggregation operators, Fuzzy Optimization & Decision Making, 3(1) (2004), 93-107.
[63] J. Ye, Multicriteria fuzzy decision-making method based on the intuitionistic fuzzy cross-entropy, 2009 International
Conference on Intelligent Human-Machine Systems and Cybernetics, 1 (2009), 59-61.
[64] X. H. Yu, Z. S. Xu, Prioritized intuitionistic fuzzy aggregation operators, Springer Berlin Heidelberg, 2007.
[65] L. A. Zadeh, Fuzzy sets, Information & Control, 8(3) (1965), 338-353.
[66] W. C. Zhang, Y. J. Xu, H. M. Wang, A consensus reaching model for 2-tuple linguistic multiple attribute group
decision making with incomplete weight information, International Journal of Systems Science, 47(2) (2016), 389-
405.
[67] H. Zhao, Z. S. Xu, Intuitionistic fuzzy multi-attribute decision making with ideal-point-based method and correlation
measure, Journal of Intelligent & Fuzzy Systems, 30(2) (2016), 747- 757.
[68] X. F. Zhao, G. W. Wei, Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to
multiple attribute decision making, Knowledge-Based Systems, 37(2) (2013), 472-479.