2,294 research outputs found
Subsethood Measures of Spatial Granules
Subsethood, which is to measure the degree of set inclusion relation, is
predominant in fuzzy set theory. This paper introduces some basic concepts of
spatial granules, coarse-fine relation, and operations like meet, join,
quotient meet and quotient join. All the atomic granules can be hierarchized by
set-inclusion relation and all the granules can be hierarchized by coarse-fine
relation. Viewing an information system from the micro and the macro
perspectives, we can get a micro knowledge space and a micro knowledge space,
from which a rough set model and a spatial rough granule model are respectively
obtained. The classical rough set model is the special case of the rough set
model induced from the micro knowledge space, while the spatial rough granule
model will be play a pivotal role in the problem-solving of structures. We
discuss twelve axioms of monotone increasing subsethood and twelve
corresponding axioms of monotone decreasing supsethood, and generalize
subsethood and supsethood to conditional granularity and conditional fineness
respectively. We develop five conditional granularity measures and five
conditional fineness measures and prove that each conditional granularity or
fineness measure satisfies its corresponding twelve axioms although its
subsethood or supsethood measure only hold one of the two boundary conditions.
We further define five conditional granularity entropies and five conditional
fineness entropies respectively, and each entropy only satisfies part of the
boundary conditions but all the ten monotone conditions
The Sun's Supergranulation
Supergranulation is a fluid-dynamical phenomenon taking place in the solar
photosphere, primarily detected in the form of a vigorous cellular flow pattern
with a typical horizontal scale of approximately 30--35~megameters, a dynamical
evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow
component and a much weaker 20--30~m/s vertical component. Supergranulation was
discovered more than sixty years ago, however, explaining its physical origin
and most important observational characteristics has proven extremely
challenging ever since, as a result of the intrinsic multiscale, nonlinear
dynamical complexity of the problem concurring with strong observational and
computational limitations. Key progress on this problem is now taking place
with the advent of 21st-century supercomputing resources and the availability
of global observations of the dynamics of the solar surface with high spatial
and temporal resolutions. This article provides an exhaustive review of
observational, numerical and theoretical research on supergranulation, and
discusses the current status of our understanding of its origin and dynamics,
most importantly in terms of large-scale nonlinear thermal convection, in the
light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new
theoretical, numerical and observational developments. All sections,
including discussion, revised extensively. Also includes previously
unpublished results on nonlinear dynamics of convection in large domains, and
lagrangian transport at the solar surfac
GRANULAR-INFORMATION-BASED RISK ANALYSIS IN UNCERTAIN SITUATIONS
In the real life almost all of the decisions that we have to make incorporate uncertainty about the future events. Assessment of the uncertainty and, thus, the risk that is inherent in these decisions models can be critical. It is even truer if we are talking about the possibility of negative impact on the environment. It is very important to assess all the environmental risks in a project if there is any hazard to the environment. In this paper the possibility of using granular information is considered. The main advantage of the granular information is that it can be used to assess risks in situations when information about future events is incomplete and imprecise. Moreover, we can use natural language to describe the problem area, as granular information paradigm uses both fuzzy and probabilistic information. We propose to use entropy as the measure of uncertainty. However, the definition of entropy should be generalised, as values of probabilities, upon which the calculation of entropy is based on, are interval-valued. We propose several possibilities of generalizing the definition of entropy. Furthermore, we analyse these approaches to see whether the additivity feature holds for the generalized entropy
Granular computing, rough entropy and object extraction
The problem of image object extraction in the framework of rough sets and granular computing is addressed. A measure called "rough entropy of image" is defined based on the concept of image granules. Its maximization results in minimization of roughness in both object and background regions; thereby determining the threshold of partitioning. Methods of selecting the appropriate granule size and efficient computation of rough entropy are described
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