32,689 research outputs found
Generalized closed sets in ditopological texture spaces with application in rough set theory
In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given
Unifying Practical Uncertainty Representations: II. Clouds
There exist many simple tools for jointly capturing variability and
incomplete information by means of uncertainty representations. Among them are
random sets, possibility distributions, probability intervals, and the more
recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of
possibility distributions. In the companion paper, we have extensively studied
a generalized form of p-box and situated it with respect to other models . This
paper focuses on the links between clouds and other representations.
Generalized p-boxes are shown to be clouds with comonotonic distributions. In
general, clouds cannot always be represented by random sets, in fact not even
by 2-monotone (convex) capacities.Comment: 30 pages, 7 figures, Pre-print of journal paper to be published in
International Journal of Approximate Reasoning (with expanded section
concerning clouds and probability intervals
Set-valued mapping and Rough Probability
In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay
concerned a rough probability by using the notion of Topology. In this paper,
we study the rough probability in the stochastic approximation spaces by using
set-valued mapping and obtain results on rough expectation, and rough variance.Comment: 9 page
Learning curves for Gaussian process regression: Approximations and bounds
We consider the problem of calculating learning curves (i.e., average
generalization performance) of Gaussian processes used for regression. On the
basis of a simple expression for the generalization error, in terms of the
eigenvalue decomposition of the covariance function, we derive a number of
approximation schemes. We identify where these become exact, and compare with
existing bounds on learning curves; the new approximations, which can be used
for any input space dimension, generally get substantially closer to the truth.
We also study possible improvements to our approximations. Finally, we use a
simple exactly solvable learning scenario to show that there are limits of
principle on the quality of approximations and bounds expressible solely in
terms of the eigenvalue spectrum of the covariance function.Comment: 25 pages, 10 figure
Exploiting Spatial Interference Alignment and Opportunistic Scheduling in the Downlink of Interference Limited Systems
In this paper we analyze the performance of single stream and multi-stream
spatial multiplexing (SM) systems employing opportunistic scheduling in the
presence of interference. In the proposed downlink framework, every active user
reports the post-processing signal-to-interference-plus-noise-power-ratio
(post-SINR) or the receiver specific mutual information (MI) to its own
transmitter using a feedback channel. The combination of scheduling and
multi-antenna receiver processing leads to substantial interference suppression
gain. Specifically, we show that opportunistic scheduling exploits spatial
interference alignment (SIA) property inherent to a multi-user system for
effective interference mitigation. We obtain bounds for the outage probability
and the sum outage capacity for single stream and multi stream SM employing
real or complex encoding for a symmetric interference channel model.
The techniques considered in this paper are optimal in different operating
regimes. We show that the sum outage capacity can be maximized by reducing the
SM rate to a value less than the maximum allowed value. The optimum SM rate
depends on the number of interferers and the number of available active users.
In particular, we show that the generalized multi-user SM (MU SM) method
employing real-valued encoding provides a performance that is either
comparable, or significantly higher than that of MU SM employing complex
encoding. A combination of analysis and simulation is used to describe the
trade-off between the multiplexing rate and sum outage capacity for different
antenna configurations
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