Parameters Estimation of Multidimensional Possibility Distributions

We present a solution to the Maxmin u/E parameters
estimation problem of possibility distributions in m-dimensional
case. Our method is based on geometrical approach, where minimal
area enclosing ellipsoid is constructed around the sample. Also we
demonstrate that one can improve results of well-known algorithms
in fuzzy model identification task using Maxmin u/E parameters
estimation.

• Sergey Sorokin
• Irina Sorokina
• Alexander Yazenin

• Possibility distribution
• parameters estimation
• Maxmin u/E estimator
• fuzzy model identification.

[1] Cai Kai-Yuan: Parameter estimations of normal fuzzy variables, Fuzzy
Sets and Systems 55 (1993) 179-185.
[2] Dug Hun Hong: Parameter estimations of mutually T-related fuzzy
variables, Fuzzy Sets and Systems 123 (2001) 6371.
[3] Wang Xizhao, Ha Minghu: Note on maxmin μ/E estimation. Fuzzy Sets
and Systems 94 (1998) 71-75.
[4] W. N¨ather, On possibilistic inference, Fuzzy Sets and Systems 36 (1990)
327-337.
[5] Wang Xizhao, Ha Minghu: Fuzzy linear regression analysis, Fuzzy Sets
and Systems 52 (1992) 179 -188.
[6] W. Zhenyuan, L. Shoumei: Fuzzy linear regression analysis of
fuzzy-valued variables, Fuzzy Sets and Systems 36 (1990) 125 - 136.
[7] Steven Nahmias: Fuzzy variables. Fuzzy Sets and Systems 1 (1978)
97-110.
[8] A.V. Yazenin: On the problem of possibilistic optimization. Fuzzy Sets
and Systems 81 (1996) 133-140.
[9] M.B. Rao, A. Rashed: Some comments on fuzzy variables. Fuzzy Sets
and Systems 6 (1981) 285-292.
[10] Hans-Peter Schr¨ocker: Uniqueness Results for Minimal Enclosing
Ellipsoids, Computer Aided Geometric Design 25, Issue 9, (December
2008) 756-762.
[11] Stephen L. Chiu: Fuzzy model identification based on cluster estimation.
Journal of Intelligent and Fuzzy Systems, Vol. 2, (1994), 267-278.
[12] A.S. Lapedes, R. Farber: Nonlinear signal processing using neural
networks: predictions and system modelling. Tech. Rep. LA-UR-87-2662,
Los Alamos Nat. Lab., Los Alamos, NM, (1987).
[13] JSR Jang: ANFIS: Adaptive-network-based fuzzy inference system.
IEEE Trans. on Systems, Man & Cybernetics 23(3), (1993), 665-685.
[14] R.S. Crowder: Predicting the Mackey-Glass time series with
cascade-correlation learning. In Proc. 1990 Connectionist Models
Summer School, Carnegie Mellon University, (1990), 117-123.