40,394 research outputs found
Parametric matroid of rough set
Rough set is mainly concerned with the approximations of objects through an
equivalence relation on a universe. Matroid is a combinatorial generalization
of linear independence in vector spaces. In this paper, we define a parametric
set family, with any subset of a universe as its parameter, to connect rough
sets and matroids. On the one hand, for a universe and an equivalence relation
on the universe, a parametric set family is defined through the lower
approximation operator. This parametric set family is proved to satisfy the
independent set axiom of matroids, therefore it can generate a matroid, called
a parametric matroid of the rough set. Three equivalent representations of the
parametric set family are obtained. Moreover, the parametric matroid of the
rough set is proved to be the direct sum of a partition-circuit matroid and a
free matroid. On the other hand, since partition-circuit matroids were well
studied through the lower approximation number, we use it to investigate the
parametric matroid of the rough set. Several characteristics of the parametric
matroid of the rough set, such as independent sets, bases, circuits, the rank
function and the closure operator, are expressed by the lower approximation
number.Comment: 15 page
Intertemporal Choice of Fuzzy Soft Sets
This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie
On Multifractal Structure in Non-Representational Art
Multifractal analysis techniques are applied to patterns in several abstract
expressionist artworks, paintined by various artists. The analysis is carried
out on two distinct types of structures: the physical patterns formed by a
specific color (``blobs''), as well as patterns formed by the luminance
gradient between adjacent colors (``edges''). It is found that the analysis
method applied to ``blobs'' cannot distinguish between artists of the same
movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8.
The method can distinguish between different types of images, however, as
demonstrated by studying a radically different type of art. The data suggests
that the ``edge'' method can distinguish between artists in the same movement,
and is proposed to represent a toy model of visual discrimination. A ``fractal
reconstruction'' analysis technique is also applied to the images, in order to
determine whether or not a specific signature can be extracted which might
serve as a type of fingerprint for the movement. However, these results are
vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps
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