7,700 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
Elliptic operators on refined Sobolev scales on vector bundles
We introduce a refined Sobolev scale on a vector bundle over a closed
infinitely smooth manifold. This scale consists of inner product H\"ormander
spaces parametrized with a real number and a function varying slowly at
infinity in the sense of Karamata. We prove that these spaces are obtained by
the interpolation with a function parameter between inner product Sobolev
spaces. An arbitrary classical elliptic pseudodifferential operator acting
between vector bundles of the same rank is investigated on this scale. We prove
that this operator is bounded and Fredholm on pairs of appropriate H\"ormander
spaces. We also prove that the solutions to the corresponding elliptic equation
satisfy a certain a priori estimate on these spaces. The local regularity of
these solutions is investigated on the refined Sobolev scale. We find new
sufficient conditions for the solutions to have continuous derivatives of a
given order.Comment: 22 page
Operator synthesis II. Individual synthesis and linear operator equations
The second part of our work on operator synthesis deals with individual
operator synthesis of elements in some tensor products, in particular in
Varopoulos algebras, and its connection with linear operator equations. Using a
developed technique of ``approximate inverse intertwining'' we obtain some
generalizations of the Fuglede and the Fuglede-Weiss theorems. Additionally, we
give some applications to spectral synthesis in Varopoulos algebras and to
partial differential equations.Comment: 42 page
Intrinsic pseudodifferential calculi on any compact Lie group
In this paper, we define in an intrinsic way operators on a compact Lie group
by means of symbols using the representations of the group. The main purpose is
to show that these operators form a symbolic pseudo-differential calculus which
coincides or generalises the (local) H\"ormander pseudo-differential calculus
on the group viewed as a compact manifold.Comment: 48 pages, with table of content
Some New Implication Operations Emerging From Fuzzy Logic
We choose, from fuzzy set theory, t-norms, t-conorms and fuzzy compliments which forms dual triplet that is (i,u,c) that satisfy the DeMorgan's law, these dual triplet are used in the construction of fuzzy implications in fuzzy logic. In this work introduction of fuzzy implication is given, which included definition of fuzzy implications and their properties and also distinct classes of fuzzy implication (S, R and QL-implications). Further also described previous work on fuzzy implication and supporting literature of construction of fuzzy implication are given. Finally main contribution of work is to design new fuzzy implication and their graphical representations
Schatten classes on compact manifolds: Kernel conditions
In this paper we give criteria on integral kernels ensuring that integral
operators on compact manifolds belong to Schatten classes. A specific test for
nuclearity is established as well as the corresponding trace formulae. In the
special case of compact Lie groups, kernel criteria in terms of (locally and
globally) hypoelliptic operators are also given.Comment: 22 page
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