By Christian Servin, Vladik Kreinovich
On quite a few examples starting from geosciences to environmental sciences, this
book explains how you can generate an sufficient description of uncertainty, tips to justify
semiheuristic algorithms for processing uncertainty, and the way to make those algorithms
more computationally effective. It explains in what feel the prevailing process to
uncertainty as a mix of random and systematic parts is barely an
approximation, offers a extra enough three-component version with an additional
periodic blunders part, and explains how uncertainty propagation ideas can
be prolonged to this version. The ebook offers a justification for a virtually efficient
heuristic process (based on fuzzy decision-making). It explains how the computational
complexity of uncertainty processing may be lowered. The e-book additionally indicates how to
take under consideration that during genuine existence, the knowledge approximately uncertainty is frequently only
partially recognized, and, on a number of sensible examples, explains easy methods to extract the missing
information approximately uncertainty from the to be had data.
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Extra resources for Propagation of Interval and Probabilistic Uncertainty in Cyberinfrastructure-related Data Processing and Data Fusion
Sample text
Let h denote the total number of such cells. This means that as the result of combining prior estimates and estimates corresponding to high spatial resolution model(s), we have h values x f ,1 , x f ,2 , . . , x f ,h . 2 Model Fusion: Case of Probabilistic Uncertainty 47 Derivation. In this case, the above system of linear equations takes the following form: for i = 1, . . , h, we have σ −2 f ,i · (xi − x f ,i ) + 1 · w1,i · 2 σl,1 ∑ w1,i · xi − X1 + i 1 (xi − X1 ) = 0; 2 σe,1 and for i > h, we have 1 · w1,i · 2 σl,1 ∑ w1,i · xi − X1 + i 1 (xi − X1) = 0.
53 Fig. 7. 3 Model Fusion: Case of Interval Uncertainty Main Idea. Our solution to the model fusion problem is to take into account three different types of approximate equalities: • Each higher spatial resolution estimate xi is approximately equal to the actual value xi in the corresponding (smaller size) cell i, with the approximation error xi − xi bounded by the known value Δh,i : xi − Δh,i ≤ xi ≤ xi + Δh,i . • Each lower spatial resolution estimate X j is approximately equal to the average of values of all the smaller cells xi(1, j) , .
A (xm ) > μi (xm ), then min(μa (xm ), μi (xm )) = μi (xm ). In this case, we cannot have μi (xm ) = 1, so we must have μi (xm ) < 1. In this case, by modifying xm a little bit, we can increase the value μi (x) and thus, achieve a larger value of the min(μa (x), μi (x)) – which contradicts to our assumption that the function attains maximum at xm . Similarly, the maximum cannot be attained when μa (xm ) < μi (xm ), so it has to be attained when μa (xm ) = μi (xm ). In this case, the desired maximum d is equal to d = μa (xm ) = μi (xm ).