4,883 research outputs found
Knowledge reduction of dynamic covering decision information systems with varying attribute values
Knowledge reduction of dynamic covering information systems involves with the
time in practical situations. In this paper, we provide incremental approaches
to computing the type-1 and type-2 characteristic matrices of dynamic coverings
because of varying attribute values. Then we present incremental algorithms of
constructing the second and sixth approximations of sets by using
characteristic matrices. We employ experimental results to illustrate that the
incremental approaches are effective to calculate approximations of sets in
dynamic covering information systems. Finally, we perform knowledge reduction
of dynamic covering information systems with the incremental approaches
Curse of dimensionality reduction in max-plus based approximation methods: theoretical estimates and improved pruning algorithms
Max-plus based methods have been recently developed to approximate the value
function of possibly high dimensional optimal control problems. A critical step
of these methods consists in approximating a function by a supremum of a small
number of functions (max-plus "basis functions") taken from a prescribed
dictionary. We study several variants of this approximation problem, which we
show to be continuous versions of the facility location and -center
combinatorial optimization problems, in which the connection costs arise from a
Bregman distance. We give theoretical error estimates, quantifying the number
of basis functions needed to reach a prescribed accuracy. We derive from our
approach a refinement of the curse of dimensionality free method introduced
previously by McEneaney, with a higher accuracy for a comparable computational
cost.Comment: 8pages 5 figure
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