However, the collapse of the distribution of possibilities inherent in the UKCP09 method into a single reference year or a small number of reference years, potentially means the loss of most of the information about the potential range of the response of the building and of the risk occupants might be subject to.
Care is taken in explaining how to implement such a technique and for estimating distributions of possibility.
The original possibility distribution of single measurements (dashed lines) and the possibility distributions computed with PMFA (solid lines) are depicted in the Figure 5. Notice that results are similar to those obtained in the previous example, where the standard linear programming framework was used (even if additional auxiliar variables ϵ2, μ2, etc. were not used).
In this case, the possibility distribution of output representing only parameter uncertainty is obtained via possibility theory.
This method avoids the complex associated computations and the further treatment of the propagation of information is easier to realize, especially because of the simple parameterized shape of possibility distribution.
For a multidimensional Δ = Δ1 × Δ2, δ = (δ1, δ2) ∈ Δ, the marginal possibility distribution of δ1 is defined as: (2) i.e., the possibility of the event { δ1 = }.
In this work, epistemic uncertainty is captured through the use of fuzzy variables, i.e. variables that are described in terms of possibility distributions.
Thus, for all model structures (M_k), (1le k le K), we have a set of possibility distributions for output variable Y, noted (pi _{Y_1} y), pi _{Y_2} y), ldots, pi _{Y_K} y)).
Since the results of simulation are in the form of possibility distributions, the DEA model is treated on a fuzzy basis; therefore, a recent possibilistic programming approach is used to convert the fuzzy DEA model to an equivalent crisp one.
Open image in new window Fig. 11 Land-cover maps Open image in new window Fig. 12 Possibility distribution of LCC prediction model output for only parameter uncertainty Open image in new window Fig. 13 Possibility distributions of LCCs for three different prediction model structures.
