This paper presents a new concept of trapezoidal cubic fuzzy numbers and solves the plant location selection (PLS) problem based on a new decision method with cubic fuzzy information captured through trapezoidal cubic fuzzy numbers. In the decision process, the unknown weights of the criteria are unearthed by using the Shannon entropy theory and the weights of the decision makers by integrating the Evidence theory with Bayes approximation. Based on trapezoidal cubic fuzzy numbers, we extend the classical VIKOR method to solve the MAGDM problems under cubic fuzzy environment based on the TrCFNs on proposed method.
ChoudharyD., ShankarR., and STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal power plant location: A case study from India, Energy42 (2012), 510–521.
4.
ChouS.Y., ChangY.H., ShenC.Y., A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes, European Journal of Operational Research189 (2008), 132–145.
5.
DuttaB., GuhaD., Trapezoidal intuitionistic fuzzy Bonferroni means and its application in multi-attribute decision making, IEEE International Conference on Fuzzy Systems (FUZZ) (2013), 1–8.
6.
DeviK., Extension of VIKOR method in intuitionist fuzzy environment for robot selection, Expert Systems with Applications38 (2011), 14163–14168.
7.
ErtugrulI., KarakasogluN., Comparison of fuzzy AHP and fuzzy TOPSIS methods for facility location selection, International Journal of Advanced Manufacturing Technology39 (2008), 783–795.
8.
HwangC.L., YoonK.L., Multiple Attribute Decision Making: Methods and Applications. Springer Verlag, New York, (1981).
9.
HwangC.L., LinM.J., Group Decision Making under Multiple Criteria: Methods and Applications. Springer Verlag, New York, (1987).
10.
JunY.B., KimC.S., YangKi.O., Cubic sets, Annals of Fuzzy Mathematics and Informatics4(1) (2012), 83–98.
11.
KaboliA., AryanezhadM.B., ShahanaghiK., Tavakkoli-MoghaddamR., A holistic approach based on MCDM for solving location problems, International Journal of Engineering Transactions A: Basics20 (2007), 251–262.
12.
LiX., ChenX., Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information, Applied Soft Computing30 (2015), 454–461.
13.
LiX., ChenX., Extension of the TOPSIS method based on prospect theory and trapezoidalintuitionistic fuzzy numbers for group decision making, Journal of Systems Science and Systems Engineering23 (2014), 231–247.
14.
OpricovicS., TzengG.H., Extended VIKOR method in comparison with outranking methods, European Journal of Operational Research178 (2007), 514–529.
15.
OpricovicS., Fuzzy VIKOR with an application to water resources planning, Expert Systems with Applications38 (2011), 12983–12990.
16.
Pavi'cI., Babi'cZ., The use of the PROMETHEE method in the location choice of aproduction system, International Journal of Production Economics23 (1991), 165–174.
17.
ShenL., WangH., FengX., Some arithmetic aggregation operators within intuitionistic trapezoidal fuzzy setting and their application to group decision making, IEEE International Conference on Management Science and Industrial Engineering (MSIE) (2011), 1053–1059.
18.
ShenF., XuJ., XuZ., An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets, Information Sciences (2015). http://dx.doi.org/10.1016/j.ins.2015.12.003.
19.
ShiY., Dynamic multi-attribute decision making model based on intuitionistic trapezoidal fuzzy numbers, 6th International Conference on Information Management, Innovation Management and Industrial Engineering (ICIII)3 (2013), 535–538.
20.
SpohrerG.A., KmakT.R., Qualitative analysis used in evaluating alternative plant location scenarios, Industrial Engineering16 (1984), 52–56.
Tavakkoli-MoghaddamR., MousaviS.M., HeydarM., An integrated AHP-VIKOR methodology for plant location selection, International Journal of Engineering Transactions B: Applications24 (2011), 127–137.
23.
VahdaniB., MousaviS.M., Tavakkoli-MoghaddamR., Plant location selection by using a three-step methodology: Delphi-AHP-VIKOR, World Academy of Science, Engineering and Technology7 (2013), 1883–1886.
24.
WanS.P., Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making, Applied Mathematical Modelling37 (2013), 4112–4126.
25.
WanS.P., WangQ.Y., DongJ.Y., The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers, Knowledge-Based Systems52 (2013), 65–77.
26.
WanS.P., DongJ.Y., Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making, Applied Soft Computing29 (2015), 153–168.
27.
WanS.P., XuG.L., WangF., DongJ.Y., A new method for Atanassovs interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information, Information Sciences316 (2015), 329–347.
28.
WangJ.Q., Overview on fuzzy multi-criteria decision-making approach, Control and Decision23 (2008), 601–606.
29.
WuJ., CaoQ.W., Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers, Applied Mathematical Modelling37 (2013), 318–327.
30.
YeJ., Multicriteria group decision-making method using the distances-based similarity measures between intuitionistic trapezoidal fuzzy numbers, International Journal of General Systems41 (2012), 729–739.
31.
YongD., Plant location selection based on fuzzy TOPSIS, International Journal of Advanced Manufacturing Technology28 (2006), 839–844.
32.
YoonK., HwangC.L., Manufacturing plant location analysis by multiple attribute decision making: Part II - multi-plant strategy, International Journal of Production Research23 (1985), 361–370.
33.
ZadehL.A., The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences8 (1975), 199–249.
34.
ZhangX., JinF., LiuP., A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number, Applied Mathematical Modelling37 (2013), 3467–3477.
