Abstract
With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, a new decision making analysis method is developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced, and the comparison method for the intuitionistic trapezoidal fuzzy numbers is proposed. Then, combined the power aggregation operator and the generalized aggregation operator, a power generalized average (PGA) operator is proposed, and some properties of the PGA operator, such as idempotency, boundary, commutativity, etc., are studied. At the same time, some special cases of the generalized parameters in PGA operator are analyzed. Furthermore, an intuitionistic trapezoidal fuzzy power generalized weighted average (ITFPGWA) operator is also proposed for the intuitionistic trapezoidal fuzzy information, and some properties of the ITFPGWA operator and an approach to deal with group decision making problems under intuitionistic trapezoidal fuzzy information based on the ITFPGWA operator are given. Finally, an illustrative example is given to illustrate the decision-making steps, and to demonstrate its practicality and effectiveness.
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References
L. A. Zadeh, Fuzzy sets, Information and Control 8(1965) 338–356.
K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1986) 87–96.
K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33(1989) 37–46.
Z.S. Xu, R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems 35(2006) 417–433.
Z.S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems 15(2007) 1179–1187.
K.T. Atanassov, G. Gargov, interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 3(1989) 343–349.
K.T. Atanassov, Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 64(1994) 159–174.
Z.S. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision 22(2007) 215–219.
Z.S. Xu, J. Chen, An approach to group decision making based on interval-valued intuitionistic judgment matrices, Systems Engineering Theory and Practice 27(2007) 26–133.
M.H. Shu, C.H. Cheng, J.R. Chang, Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelectronics Reliability 46(2006) 2139–2148.
X. Zhang, P.D. Liu, Method for aggregating triangular intuitionistic fuzzy information and its application to decision making, Technological and Economic Development of Economy 16(2010) 280–290.
J.Q. Wang, Overview on fuzzy multi-criteria decisionmaking approach, Control and Decision 23(2008) 601–606.
J.Q. Wang, Z.H. Zhang, Programming method of multicriteria decision-making based on intuitionistic fuzzy number with incomplete certain information, Control and Decision 23(2008) 1145–1148.
J.Q. Wang, Z.H. Zhang, Multi-criteria decision-making method with incomplete certain information based on intuitionistic fuzzy number, Control and Decision 24(2009) 226–230.
J.Q. Wang, Z.H. Zhang, Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems, Journal of Systems Engineering and Electronics 20(2009) 321–326.
S.P. Wan, J.Y. Dong, Method of intuitionistic trapezoidal fuzzy number for multi-attribute group decision, Control and Decision 25(2010) 773–776.
G.W. Wei, Some Arithmetic Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers and Their Application to Group Decision Making, Journal of Computers 5(2010) 345–351.
R.R. Yager, Generalized OWA aggregation operators, Fuzzy Optimization and Decision Making 3(2004) 93–107.
D.F. Li, Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets, Expert Systems with Applications 37(2010) 8673–8678.
H. Zhao, Z.S. Xu, M. Ni, S. Liu, Generalized aggregation operators for intuitionistic fuzzy sets, International Journal of Intelligent Systems 25(2010) 1–30.
J.M. Merigó, M. Casanovas, The Generalized Hybrid Averaging Operator and its Application in Decision Making, Journal of Quantitative Methods for Economics and Business Administration 9(2010) 69–84.
J.M. Merigó, M. Casanovas, Fuzzy generalized hybrid aggregation operators and its application in decision making, International Journal of Fuzzy Systems 12(1) (2010) 15–24.
R.R. Yager, The power average operator, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 31(2001) 724–731.
Z.S. Xu, R.R. Yager, Power-geometric operators and their use in group decision making, IEEE Tra nsactions on Fuzzy Systems 18(2010) 94–105
Z.S. Xu, Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators, Knowledge-Based Systems 24(2011) 749–760.
Y.J. Xu, H.M Wang, Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment, Applied Soft Computing 11(2011) 3988–3997.
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Liu, P., Liu, Y. An Approach to Multiple Attribute Group Decision Making Based on Intuitionistic Trapezoidal Fuzzy Power Generalized Aggregation Operator. Int J Comput Intell Syst 7, 291–304 (2014). https://doi.org/10.1080/18756891.2013.862357
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DOI: https://doi.org/10.1080/18756891.2013.862357