Comparing fuzzy numbers is a key task in decision making. Although, up to now several techniques have been introduced for ordering fuzzy numbers, nearly all of these methods contain various defects. In this paper, we introduce a new approach for ranking generalized trapezoidal fuzzy numbers. The suggested technique combines the trait of two ideas namely positive and negative ideal points as well as the centroid point. This method is logically easy and has very straightforward computation. The benefits of the proposed method are discussed through a number of comparative numerical cases.
AbbasbandyS. and HajjariT., A new approach for ranking of trapezoidal fuzzy numbers, Computers and Mathematics with Applications57 (2009), 413–419.
2.
AsadyB., The revised method of ranking LR fuzzy number based on deviation degree, Expert Systems with Applications37 (2010), 5056–5060.
3.
AsadyB., and ZendehnamM., Ranking of fuzzy numbers by minimize distance, Applied Mathematical Modelling31 (2007), 2589–2598.
4.
BakarA.S.A. and GegovA., Ranking of fuzzy numbers based on centroid point and spread, Journal of Intelligent & Fuzzy Systems27 (2014), 1179–1186.
5.
ChenS.H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems17 (1985), 113–129.
6.
ChenS.M., Evaluating weapon systems using fuzzy arithmetic operations, Fuzzy Sets and Systems77 (1996), 265–276.
7.
ChenS.J. and ChenS.M., Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE transactions on fuzzy systems11 (2003), 45–56.
8.
ChenS.M. and ChenJ.H., Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, Expert Systems with Applications36 (2009), 6833–6842.
9.
ChenS.M. and SanguansatK., Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers, Expert Systems with Applications38 (2011), 2163–2171.
10.
ChenC.C. and TangH.C., Ranking of nonnormal p-norm trapezoidal fuzzy numbers with integral value, Computers and Mathematics with Applications56 (2008), 2340–2346.
11.
ChenS.J. and HwangC.L., Springer, Fuzzy Multiple Attribute Decision Making1992–Berlin.
12.
ChengC.H., A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and System95 (1998), 307–317.
13.
ChuT.C. and TsaoC.T., Ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications43, 111–117.
14.
DatL.Q., YuV.F. and ChouS.Y., An improved ranking method for fuzzy numbers based on the centroid index, International Journal of Fuzzy Systems14 (2012), 413–419.
15.
EzzatiR., AllahviranlooT., KhezerlooS. and KhezerlooM., An approach for ranking of fuzzy numbers, Expert Systems with Applications39 (2012), 690–695.
16.
JainR., A procedure for multi-aspect decision making using fuzzy sets, International Journal of Systems Science8 (1978), 1–7.
17.
HajjariT. and AbbasbandyS., A note on “the revised method of ranking LR fuzzy number based on deviation degree”, Expert Systems with Applications38(10) (2011), 13491–13492.
18.
KumarA., SinghP., KaurP. and KaurA., A new approach for ranking nonnormal p-norm trapezoidal fuzzy numbers, Computers & Mathematics with Applications61 (2011a), 881–887.
19.
KumarA., SinghP., KaurP. and KaurA., A new approach for ranking of L–R type generalized fuzzy numbers, Expert Systems with Applications38 (2011b), 10906–10910.
20.
LiouT.S. and WangM.J.J., Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems50 (1992), 247–255.
21.
NasseriS.H., ZadehM.M. and KardoostM.E., Behmanesh, Ranking fuzzy quantities based on the angle of the reference functions, Applied Mathematical Modelling37 (2013), 9230–9241.
22.
NejadA.M. and MashinchiM., Ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number, Computers & Mathematics with Applications61 (2011), 431–442.
23.
OpricovicS., Fuzzy VIKOR with an application to water resources planning, Expert Systems with Applications38 (2011), 12983–12990.
24.
RamliN. and MohamadD., A comparative analysis of centroid methods in ranking fuzzy numbers, European Journal of Science Research28 (2009), 492–501.
25.
RezvaniS., Ranking generalized exponential trapezoidal fuzzy numbers based on variance, Applied Mathematics and computation262 (2015), 191–198.
26.
VincentF.Y. and DatL.Q., An improved ranking method for fuzzy numbers with integral values, Applied Soft Computing14 (2014), 603–608.
27.
WangX. and KerreE.E., Reasonable properties for the ordering of fuzzy quantities, Fuzzy Sets and Systems118 (2001), 375–385.
28.
WangY.J. and LeeS.H., The revised method of ranking fuzzy numbers with an area between the centroid and original points, Computers and Mathematics with Applications55 (2008), 2033–2042.
29.
WangZ.X., LiuY.J., FanZ.P. and FengB., Ranking LR fuzzy number based on deviation degree, Information Sciences179 (2009), 2070–2077.
30.
WangY.M. and LuoY., Area ranking of fuzzy numbers based on positive and negative ideal points, Computers & Mathematics with Applications58 (2009), 1769–1779.
31.
WangY.M., YangJ.B., XuD.L. and ChinK.S., On centroids of fuzzy numbers, Fuzzy Sets and Systems157 (2006), 919–926.
32.
XuP., SuX., WuJ., SunX., ZhangY. and DengY., A note on ranking generalized fuzzy numbers, Expert Systems with Applications39 (2012), 6454–6457.
33.
YagerR.R., Ranking fuzzy subsets over the unit interval, In Proceedings of 17th IEEE International Conference on Decision and Control, San Diego, California, 1978.
34.
ZhuK., Fuzzy analytic hierarchy process: Fallacy of the popular methods, European Journal of Operational Research236 (2014), 209–217.
