In this case, the possibility distribution of output representing only parameter uncertainty is obtained via possibility theory.
Figure 12 shows the possibility distribution of output representing only parameter uncertainty based on 10,000 samples.
Figure 5 shows the possibility distribution of the LCC prediction model output, where only parameter uncertainty is propagated.
In summary, the possibility distribution has the ability to handle both aleatory and epistemic uncertainty of pixel detection through a possibility and a necessity measures.
The possibility distribution (pi _Y y)) of (Y = f (X_1, X_2, ldots, X_n)) is constructed as the collection of the values (underline{y}_alpha ) and (overline{y}_alpha ) for each (alpha ) cut. .
end{aligned} (5)The possibility distribution (pi _Y y)) of (Y = f (Y_1, Y_2, ldots, Y_K)) is constructed as the collection of the values (underline{y}^_alpha ) and (overline{y}^_alpha ) for each (alpha ) cut.
Finally, it will be shown how (linear) optimisation problems will be able to settle queries about the most possible fluxes, the possibility distributions, etc.
Figure 13 shows the possibility distributions of output representing parameter uncertainty through three different model structures.
In this framework, the possibility distributions of the model outputs are used to derive the prediction uncertainty bounds.
Select the (alpha ) cuts (A^{X1}_alpha, A^{X2}_alpha,, A^{Xj}_alpha, ldots, A^{Xn}_alpha ) of the possibility distributions (pi _{X_1}(x_1), pi _{X_2}(x_2), ldots, pi _{X_j}(x_j), ldots, pi _{X_n}(x_n)) of the possibilistic parameters (X_j), (j = 1, 2, ldots, n,) as intervals of possible values (lfloor underline{x}_{j,alpha }, overline{x}_{j,alpha } rfloor ) (j = 1, 2, ldots, n).
Select the (alpha ) cuts (A^{X1}_alpha, A^{X2}_alpha,, A^{Xj}_alpha, ldots, A^{Xn}_alpha ) of the possibility distributions (pi _{X_1}(x_1), pi _{X_2}(x_2), ldots, pi _{X_j}(x_j), ldots, pi _{X_n}(x_n)) of the possibilistic parameters (X_j), (j = 1, 2, ldots, n,) as intervals of possible values (lfloor underline{x}_{j,alpha }, overline{x}_{j,alpha } rfloor ) (j = 1, 2, ldots, n). 3.
