A Multiple Attribute Group Decision Making Method Based on 2-D Uncertain Linguistic Weighted Heronian Mean Aggregation Operator

Weihua Liu, HaiBo Liu, LingLing Li

Abstract


2-Dimension uncertain linguistic variables can describe both subjective evaluation result of attributes and reliability of the evaluation results in multiple attribute decision making problems. However, it is difficult to aggregate these evaluation information and give comprehensive results. Heronian mean (HM) has the characteristic of capturing the correlations between aggregated arguments and is extended to solve this problem. The 2-dimension uncertain linguistic weighted HM aggregation( 2DULWHMA) operator is employed in this paper. Firstly, the definition, properties, expectations and the operational laws the 2-dimension uncertain linguistic variables are investigated. Furthermore, the properties of the 2DULWHMA operators, such as commutativity, idempotency and monotonicity, etc. are studied. Some special cases of the generalized parameters in these operators are analyzed. Finally, an example is given to demonstrate the effectiveness and feasibility of the proposed method.

Keywords


2-Dimension (2-D) uncertain linguistic variables; Heronian mean; aggregation operator.

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References


Churchman C.W., Ackoff R.L., Arnoff E.L. (1975); Introduction to operations research, Wiley, New York, 1975.

Wang X.Z., Dong C.R. (2009); Improving generalization of fuzzy if then rules by maximizing fuzzy entropy, IEEE Transactions on Fuzzy Systems, 17(3):556-567.
https://doi.org/10.1109/TFUZZ.2008.924342

Xi-Zhao Wang, Ling-Cai Dong, Jian-Hui Yan(2012); Maximum Ambiguity-Based Sample Selection in Fuzzy Decision Tree Induction. IEEE Transactions on Knowledge & Data Engineering,24(8):1491-1505.DOI:10.1109/TKDE.2011.67.
https://doi.org/10.1109/TKDE.2011.67

Wang X.Z. et al. (2014); A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning, IEEE Transactions on Fuzzy Systems, 23(5):1638 - 1654. DOI:10.1109/TFUZZ.2014.237147.

Bingsheng Liu et al. (2014); A complex multi-attribute large-group decision making method based on the interval-valued intuitionistic fuzzy principal component analysis model.Soft Comput, 18:2149-2160, DOI 10.1007/s00500-013-1190-8.
https://doi.org/10.1007/s00500-013-1190-8

M. Delgado, J.L. Verdegay, M.A. Vila (1993); On aggregation operations of linguistic labels, International Journal of Intelligent Systems,8:351-370.
https://doi.org/10.1002/int.4550080303

F. Herrera-Martinez(2000); A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems,8(6):746-752.
https://doi.org/10.1109/91.890332

Liu P.D., Chen Y.B., Chu Y.C., (2014); Intuitionistic uncertain linguistic weighted bonferroni owa operator and its application to multiple attribute decision making, Cybernetics and Systems, 45(5):418-438, DOI:10.1080/01969722.2014.929348.
https://doi.org/10.1080/01969722.2014.929348

Liu P.D., Chu Y.C., Li Y.W. (2015); The multi-attribute group decision-making method based on the interval grey uncertain linguistic variable generalized hybrid averaging operator, Neural Comput Appl, 26(6):1395-1405.
https://doi.org/10.1007/s00521-014-1814-7

Liu X. et al. (2016); A New Interval-valued 2-Tuple Linguistic Bonferroni Mean Operator and Its Application to Multiattribute Group Decision Making, Int. J. Fuzzy Syst,12: 1- 23.DOI:10.1007/s40815-015-0130-4.
https://doi.org/10.1007/s40815-015-0130-4

Liu P.D., Chen Y.B., Chu Y.C. (2014); Intuitionistic uncertain linguistic weighted bonferroni owa operator and its application to multiple attribute decision making, Cybernetics and Systems, 45(5):418-438, DOI:10.1080/01969722.2014.929348
https://doi.org/10.1080/01969722.2014.929348

Liu P.D., Shi L.L. (2015); Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making, J Appl Anal Comput, 5(4):534-561.

Liu P.D., Wang Y.M. (2014); Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput, 17:90- 104.
https://doi.org/10.1016/j.asoc.2013.12.010

Liu P.D., Yu X.C. (2014); 2-Dimension uncertain linguistic power generalized weighted aggregation operator and its application in multiple attribute group decision making, Knowl Based Syst, 57:69-80.
https://doi.org/10.1016/j.knosys.2013.12.009

Zhu W.D., Zhou G.Z., Yang S.L. (2009); An approach to group decision making based on 2-dimension linguistic assessment information, Syst Eng, 27:113-118.

Liu P.D., Zhang X. (2012); An Approach to Group Decision Making Based on 2-dimension Uncertain Linguistic Assessment Information, Technol Econ Dev Econ, 18(3):424-437.
https://doi.org/10.3846/20294913.2012.702139

Liu P., He L., Yu X. (2016); Generalized Hybrid Aggregation Operators Based on the 2- Dimension Uncertain Linguistic Information for Multiple Attribute Group Decision Making, Group Decision and Negotiation,25(1):103-126, DOI:10.1007/s10726-015-9434-x
https://doi.org/10.1007/s10726-015-9434-x

Liu P.D., Qi X.F. (2014); Some generalized dependent aggregation operators with 2- dimension linguistic information and their application to group decision making, J Intell Fuzzy Syst, 27:1761-1773.

Liu P., Teng F.(2016); Multiple attribute decision-making method based on 2-dimension uncertain linguistic density generalized hybrid weighted averaging operator, Soft Comput, 10(3): 1-14, DOI 10.1007/s00500-016-2384-7.
https://doi.org/10.1007/s00500-016-2384-7

Liu P.,Wang Y.(2015); The aggregation operators based on the 2-dimension uncertain linguistic information and their application to decision making.Mach. Learn. & Cyber, 1-18, DOI:10.1007/s13042-015-0430-x.
https://doi.org/10.1007/s13042-015-0430-x

Yu X.H., Xu Z.S., Liu S.S., Chen Q. (2012); Multi-criteria decision making with 2-dimension linguistic aggregation techniques, Int J Intell Syst, 27:539-562.
https://doi.org/10.1002/int.21535

P.D. Liu, X. Zhang(2012); Intuitionistic uncertain linguistic aggregation operators and their application to group decision making, Systems Engineering-Theory & Practice, 32(12): 2704- 2711.

Z.S. Xu (2006); Goal programming models for multiple attribute decision making under linguistic setting, Journal of Management Sciences in China, 9(2): 9- 17.

Xu Z. (2006); A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision making with linguistic information. Group Decision and Negotiation, 15(6), 593-604.
https://doi.org/10.1007/s10726-005-9008-4

Beliakov G., Pradera A., Calvo T. (2007); Aggregation Functions: A Guide for Practitioners, Springer Berlin Heidelberg.

Yu D. (2013); Intuitionistic fuzzy geometric heronian mean aggregation operators, Applied Soft Computing, 13(2): 1235-1246, DOI: 10.1016/j.asoc.2012.09.021
https://doi.org/10.1016/j.asoc.2012.09.021




DOI: https://doi.org/10.15837/ijccc.2017.2.2792



Copyright (c) 2017 Weihua Liu, HaiBo Liu, LingLing Li

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