Abstract
Multi-criteria group decision making is a widely used efficient decision methodology to improve quality of the decision. In this paper, the interval-valued intuitionistic fuzzy weighted arithmetic average operator, the interval-valued intuitionistic fuzzy weighted geometric average operator, and an accuracy function of interval-valued intuitionistic fuzzy value are introduced. The proposed aggregation operators with a accuracy function is more efficient to take decision. Finally, an example is provided to illustrate the application of the developed approach. The results show that the proposed new approach is more comprehensive and flexible by comparing with the other existing aggregation operators and accuracy functions.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41478-018-0122-5/MediaObjects/41478_2018_122_Fig1_HTML.png)
Similar content being viewed by others
References
Atanassov, K. 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20: 87–96.
Atanassov, K. 1994. Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 64: 159–174.
Atanassov, K., and G. Gargov. 1989. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31: 343–349.
Chen, S.M., and J.M. Tan. 1994. Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67: 163–172.
Chen, N.A., Xu Zeshi, and Meimei Xia. 2013. Interval valued hesitant preference relations and their applications to group decision making. Knowledge Based Systems 37: 528–540.
Goraleczany, M.B. 1987. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 21: 1–17.
Herrera, F., and E. Herrera-Viedma. 2000. Linguistic decision analysis-Steps for solving decision problems under linguistic information. Fuzzy Sets and Systems 114: 103–113.
Jun, Y. 2009. Multicriteria fuzzy decision-making based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Systems with Applications 36: 6899–6902.
Lakshmana, G.N., S. Jeevaraj, and P. Dhanasekaran. 2017. An intuitionistic fuzzy multi-criteria decision making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets. Soft Computing 21: 7077–7082.
Lakshmana, G.N.V., S. Muralikrishnan, and Geetha Sivaraman. 2011. Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Systems with Applications 38: 1464–1467.
Lakshmana, G.N.V., G. Venkateshwari, and G. Sivraman. 2008. Ranking of intuitionistic fuzzy numbers. In Proceedings of the IEEE International Conference on Fuzzy Systems (IEEE Fuzz 2008), 1971–1974.
Liu, H.W., and G.J. Wang. 2007. Multicriteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research 179: 220–233.
Mitchell, H.B. 2004. Ranking intuitionistic fuzzy numbers. Fuzziness and Knowledge Based Systems, International Journal of Uncertainty 12: 377–386.
Qiu, J., and L. Li. 2017. A new approach for multiattribute group decision making with interval-valued intuitionistic fuzzy information. Applied Soft Computing 61: 111–121.
Turksen, B. 1986. Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems 20: 191–210.
Xu, Z.S. 2005. An overview of methods for determining OWA weights. International Journal of Intelligent systems 20: 843–865.
Xu, Z.S. 2007. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems 15: 1179–1187.
Xu, Z.S. 2007. Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision 22: 215–219.
Xu, Z.S. 2007. Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optimization and Decision Making 6: 109–121.
Xu, Z.S. 2010. A distance measure based method for interval-valued intuitionistic fuzzy multi-attribute group decision making. Information Sciences 180: 181–190.
Xu, Z.S. 2013. Compatibility analysis of intuitionistic fuzzy preference relations in group decision making. Group Decision and Negotiation 22: 463–482.
Xu, Z.S., and J. Chen. 2007. An approach to group decision making based on interval-valued intuitionistic fuzzy judgment matrices. System Engineer-Theory and Practice 27: 126–133.
Xu, Z.S., and J. Chen. 2007. On geometric aggregation over interval-valued intuitionistic fuzzy information. In The 4th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD07), Haikou, China, 466–471.
Xu, Z.S., and Q.L. Da. 2003. An overview of operators for aggregating information. International Journal of Intelligent Systems 18: 953–969.
Xu, Z.S., and C. Xiaoqiang. 2012. Intuitionistic Fuzzy Information Aggregation Theory and Applications. Beijing: Springer, Science Press.
Xu, Z.S., and R.R. Yager. 2006. Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General System 35: 417–433.
Ye, J. 2007. Improved method of multicriteria fuzzy decision-making based on vague sets. Computer-Aided Design 39: 164–169.
Zadeh, L.A. 1965. Fuzzy sets. Information and Control 8: 338–353.
Zhao, H., Z.S. Xu, M.F. Ni, et al. 2010. Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems 25: 1–30.
Zeng, S.Z., and W.H. Su. 2011. Intuitionistic fuzzy ordered weighted distance operator. Knowledge-Based Systems 24: 124–1232.
Zeng, S., J.M. Merigi, D.P. Marques, H. Jin, and F. Gu. 2016. Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making. Journal of Intelligent and Fuzzy Systems 32: 11–22.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
No conflicts of interest to declare.
Rights and permissions
About this article
Cite this article
Priyadharsini, J., Balasubramaniam, P. Multi-criteria decision making method based on interval-valued intuitionistic fuzzy sets. J Anal 27, 259–276 (2019). https://doi.org/10.1007/s41478-018-0122-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41478-018-0122-5
Keywords
- Interval-valued intuitionistic fuzzy set
- Arithmetic operator
- Geometric operator
- Accuracy function
- Multi-criteria fuzzy decision making