Fig. 1. Takagi function and its modified version with b=2^−0.8 and D=1.2.

Fig. 2. WM function with different H(b=2.1).

Fig. 3. An example of box-counting method.

Fig. 4. An example of BM method.

Fig. 5. Weight of D_e(Lm(i), n).

Fig. 6. An example of the input variable DENS_h.

Fig. 7. The rough degree RD and the curve E. (a)  An example of RD with SW=3, (b) Generating E for WM function with b=2.1 and D=1.5.

Fig. 8. General scheme of the proposed estimator.

Fig. 9. Recursive definition of activation and inhibition hyperboxes.

Fig. 10. Trapezoidal membership function for μ_Z(x_k, γ_k).

Fig. 11. Gaussian membership function for μ_Z(x_k, γ_k).

Fig. 12. Evolution of the averaged errors with D for the WM function (Q=500−SW=100).

Fig. 13. Evolution of the averaged error with D for the Takagi function (Q=500−SW=100).

Fig. 14. (a) A 3D AFM image of a wool fiber. (b) A 2D AFM image of the same fiber.(c) Two profiles (F_150 and F_170) extracted from the fiber.

Fig. 15. Two profiles of a polypropylene Fiber.

Table 1. An example of box counting estimation errors for WM functions with n=10

Table 2. Pertinence analysis of input variables

Table 3. Fractal dimensions of the profiles of the wool fiber calculated from different methods

Table 4. Fractal dimensions of the profiles of the polypropylene fiber calculated from different methods