In this paper, the problem of ranking multi-dimensional uncertain information based on fuzzy order is studied. At first, a specific fuzzy order on the fuzzy ellipsoid number space is defined, with which we can set up a dynamic ranking method which changes with the change of the level r for some objects which can be characterized by some multichannel uncertain digital information. Then its properties are investigated, some related results are obtained. And then, we give a practical example to show how to set up a dynamic ranking method which changes with the change of the level r for some objects which can be characterized by some multichannel uncertain digital information by using the fuzzy order proposed by us in the paper.
D.Arotaritei and F.Ionescu, Fuzzy Voronoi diagram for disjoint fuzzy numbers of dimension two, Journal of Intelligent and Fuzzy Systems26 (2014), 1253–1262.
2.
B.Asady, Revision of distance minimization method for ranking of fuzzy numbers, Applied Mathematical Modelling35(3) (2011), 1306–1313.
3.
D.Butnariu, Methods of solving optimization problems and linear equations in the space of fuzzy vectors, Libertas Math17 (1997), 1–7.
4.
S.S.L.Chang and L.A.Zadeh, On fuzzy mappings and control, IEEE Trans Syst Man Cybernet2 (1972), 30–34.
5.
L.Coroianu, M.Gagolewski and P.Grzegorzewski, Nearest piecewise linear approximation of fuzzy numbers, Fuzzy Sets and Systems233 (2014), 26–51.
6.
H.Deng, Comparing and ranking fuzzy numbers using ideal solutions, Applied Mathematical Modelling38(5-6) (2014), 1638–1646.
7.
P.Diamond and P.Kloeden, Metric Space of Fuzzy Sets, World Scientific, Singapore, 1994.
8.
D.Dubois and H.Prade, Operations on fuzzy numbers, Internat J Systems Sci9 (1978), 613–626.
9.
D.Dubois and H.Prade, Towards fuzzy differential calculus-Part I, II, III, Fuzzy Sets and Systems8 (1982), 1–17, 105–116, 225–234.
10.
R.Eslamipoor, M.J.Haji and A.Sepehriar, Proposing a revised method for ranking fuzzy numbers, Journal of Intelligent and Fuzzy Systems25 (2013), 373–378.
11.
R.Goetschel and W.Voxman, Elementary calculus, Fuzzy Sets and Systems18 (1986), 31–43.
12.
Q.Gu and Z.Xuan, A new approach for ranking fuzzy numbers based on possibility theory, Journal of Computational and Applied Mathematics309 (2017), 674–682.
13.
M.J.Haji, H.K.Zare, R.Eslamipoor and A.Sepehriar, A developed distance method for ranking generalized fuzzy numbers, Neural Comput and Applic25 (2014), 727–731.
14.
D.H.Hong, The law of large numbers and renewal process for T-related weighted fuzzy numbers on Rp, Information Sciences228 (2013), 45–60.
15.
A.Kaufmann and M.M.Gupta, Introduction to Fuzzy Arithmetic-Theory and Applications, Van Nostrand, Reinhold, NY, 1985.
16.
J.D.Kim, E.L.Moon, E.Jeong and D.H.Hong, Ranking methods for fuzzy numbers: The solution to Brunelli and Mezei's conjecture, Fuzzy Sets and Systems315 (2017), 109–113.
17.
J.Moreno-Garcia, L.J.Linares, L.Rodriguez-Benitez and E.D.Castillo, Fuzzy numbers from raw discrete data using linear regression, Information Sciences233 (2013), 1–14.
18.
G.Wang and Y.Li, Ranking of multidimensional uncertain information based on metrics on the fuzzy ellipsoid number space, IEEE Trans on Fuzzy Systems25(3) (2017), 614–626.
19.
G.Wang, Y.Li and C.Wen, On fuzzy n–cell numbers and n–dimension fuzzy vectors, Fuzzy Sets and Systems158 (2007), 71–84.
20.
G.Wang, P.Shi, R.K.Agarwal and Y.Shi, On fuzzy ellipsoid numbers and membership functions, Journal of Intelligent & Fuzzy Systems31 (2016), 391–403.
21.
G.Wang, P.Shi and P.Messenger, Representation of uncertain multi-channel digital signal spaces and study of pattern recognition based on metrics and diferrence values on fuzzy n-ell number spaces, IEEE Trans on Fuzzy Systems17(2) (2009), 421–439.
22.
G.Wang, P.Shi and P.Messenger, Weak orders on multichannel information spaces and their applications in evaluating, IMA Journal of Mathematical Control and Information2012 (2012), 357–381.
23.
G.Wang, P.Shi, B.Wang and J.Zhang, Fuzzy n-ellipsoid numbers and representations of uncertain multichannel digital information, IEEE Trans on Fuzzy Systems22(5) (2014), 1113–1126.
24.
G.Wang and C.Wu, Fuzzy n–cell numbers and the differential of fuzzy n–cell number value mappings, Fuzzy Sets and Systems130 (2002), 367–381.
25.
H.S.Yazdi, M.GhasemiGol and S.Effati, Hierarchical tree clustering of fuzzy number, Journal of Intelligent and Fuzzy Systems26 (2014), 541–550.
