20,666 research outputs found
Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology
Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted.
The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing
Evolving fuzzy CP^n and lattice n-simplex
Generalizing the previous works on evolving fuzzy two-sphere, I discuss
evolving fuzzy CP^n by studying scalar field theory on it. The space-time
geometry is obtained in continuum limit, and is shown to saturate locally the
cosmic holographic principle. I also discuss evolving lattice n-simplex
obtained by `compactifying' fuzzy CP^n. It is argued that an evolving lattice
n-simplex does not approach a continuum space-time but decompactifies into an
evolving fuzzy CP^n.Comment: Typos corrected, 13 pages, no figures, LaTe
Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills
(SYM) theory and deform it by a mass parameter M with keeping all supercharges.
We further add another mass parameter m in a manner to respect two of the eight
supercharges and put the deformed theory on a two-dimensional square lattice,
on which the two supercharges are exactly preserved. The flat directions of
scalar fields are stabilized due to the mass deformations, which gives discrete
minima representing fuzzy spheres. We show in the perturbation theory that the
lattice continuum limit can be taken without any fine tuning. Around the
trivial minimum, this lattice theory serves as a non-perturbative definition of
two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice
theory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around the
minimum of k-coincident fuzzy spheres.Comment: 35 pages, LaTeX2e, final version accepted in Nucl. Phys.
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