Interval-valued intuitionistic fuzzy aggregation methodology for decision making with a prioritization of criteria

Document Type: Research Paper

Authors

1 School of Economics and Management, Guangxi Normal University, Guilin 541004, China

2 Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564, USA

Abstract

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.
The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.
Based on the ${\L}$ukasiewicz triangular norm, we first propose a prioritized arithmetic mean to IVIF multi-criteria decision making (MCDM) problem where there is a linear ordering among the criteria.
The proposed aggregation operator overcomes the existing prioritized aggregation operator's shortcomings that it is not monotone with respect to the total order on interval-valued intuitionistic fuzzy values (IVIFVs).
We also prove that it is bounded and monotone with respect to the total order on IVIFVs, and therefore is a true generalization of such operations.
We finally propose an aggregation operators-based two-step procedure to IVIF MCDM in the situation that more than one criteria exist at some priority level.

Keywords


[1] K. T. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(3) (1989), 343–349.
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87–96.
[3] G. Beliakov, H. Bustince, D. P. Goswami, U. K. Mukherjee, N. R. Pal, On averaging operators for Atanassov's
intuitionistic fuzzy sets, Information Sciences, 181(6) (2011), 1116–1124.
[4] H. Bustince and P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 78(3) (1996),
293–303.
[5] T.-Y. Chen, A prioritized aggregation operator-based approach to multiple criteria decision making using interval-
valued intuitionistic fuzzy sets: A comparative perspective, Information Sciences, 281 (2014), 97–112.
[6] G. Deschrijver, E. E. Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy Sets and Systems, 136(3)
(2003), 333–361.

[7] G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems,
133(2) (2003), 227–235.
[8] G. Deschrijver, E. E. Kerre, On the position of intuitionistic fuzzy set theory in the framework of theories modelling
imprecision, Information Sciences, 177(8) (2007), 1860–1866.
[9] C. L. Hwang, K. Yoon, Multiple attribut decision making : Methods and applications, Springer, Berlin, Heidelberg,
1981.
[10] Y. Li, Y. Deng, Felix T. S. Chan, J. Liu, X. Deng, An improved method on group decision making based on interval-
valued intuitionistic fuzzy prioritized operators, Applied Mathematical Modelling, 38(9-10) (2014), 2689–2694.
[11] W. Liu, S.-H. Yang, A novel method for multi-attribute group decision making with interval-valued intuitionistic
uncertain linguistic information based on topsis, In: Proceedings of 2014 International Conference On Management
Science & Engineering (ICMSE), 193–199, Piscataway, NJ, USA, 2014.
[12] W. Wang, X. Liu, Y. Qin, Interval-valued intuitionistic fuzzy aggregation operators, Journal of Systems Engineering
and Electronics, 23(4) (2012), 574–580.
[13] Z. Wang, K. W. Li, W. Wang, An approach to multiattribute decision making with interval-valued intuitionistic
fuzzy assessments and incomplete weights, Information Sciences, 179(17) (2009), 3026–3040.
[14] H.Wu, X. Su, Interval-valued intuitionistic fuzzy prioritized hybrid weighted aggregation operator and its application
in decision making, Journal of Intelligent & Fuzzy Systems, 29(4) (2015), 1697–1709.
[15] Z. S. Xu, J. Chen, On geometric aggregation over interval-valued intuitionistic fuzzy information, In: Proceedings
of Fourth International Conference on Fuzzy Systems and Knowledge Discovery, Piscataway, NJ, USA, 2 (2007),
466–471.
[16] R. R. Yager, Modeling prioritized multicriteria decision making, IEEE Transactions on Systems, Man, and Cybernetics,
Part B (Cybernetics), 34(6) (2004), 2396–2404.
[17] R. R. Yager, Prioritized OWA aggregation, Fuzzy Optimization and Decision Making, 8(3) (2009), 245–262.
[18] R. R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning, 48(1) (2008),
263–274.
[19] D. Yu, Y.Wu, T. Lu, Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision
making, Knowledge-based Systems, 30 (2012), 57–66.
[20] C. Yue, A geometric approach for ranking interval-valued intuitionistic fuzzy numbers with an application to group
decision-making, Computers & Industrial Engineering, 102 (2016), 233–245.
[21] C. Yue, Entropy-based weights on decision makers in group decision-making setting with hybrid preference repre-
sentations, Applied Soft Computing, 60 (2017), 737–749.
[22] C. Yue, Two normalized projection models and application to group decision-making, Journal of Intelligent & Fuzzy
Systems, 32(6) (2017), 4389–4402.
[23] Z. Yue, An avoiding information loss approach to group decision making, Applied Mathematical Modelling, 37(1-2)
(2013), 112–126.
[24] Z. Yue, Group decision making with multi-attribute interval data, Information Fusion, 14(4) (2013), 551–561.
[25] Z. Yue, Topsis-based group decision-making methodology in intuitionistic fuzzy setting, Information Sciences, 277
(2014), 141–153.
[26] Z. Yue, Y. Jia, An application of soft computing technique in group decision making under interval-valued intu-
itionistic fuzzy environment, Applied Soft Computing, 13(5) (2013), 2490–2503.
[27] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338–353.
[28] M. Zeleny, Multiple criteria decision making, McGraw-Hill, New York, 1982.