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The cost of a route is a set function mapping a subset of edges, vessel types and quantities to deploy to the set of non-negative real numbers.
A set function ℳ is called an uncertain measure if it satisfies the following axioms.
Definition 4. A set function is additive if there exist nonnegative real numbers such that for each.
A set function is XOS, if there are additive value functions for some positive integer such that (15).
The letter X will be reserved for elements of ({mathcal{S}}), and P is a set function derived from E as in (5).
A set function (mathcal{M}) defined on the σ-algebra (mathcal{L}) over Γ is called an uncertain measure if it satisfies the following three axioms.
Similar(36)
Instead of associating a level set function with a specific fluid material, the function is associated with a pair of materials and the interface that separates them.
Letbandpbe a submodular and a supermodular set function onVsuch thatp(X)≤b(X) for allX⊆V.
Level set methods use a level set function, usually an approximate signed distance function, Φ, to represent the interface as the zero set of Φ.
Consider a level set function Ψ that has a contour in the form of the desired shape prior.
A level set function is used to provide a precise position of the interfaces.
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