14,157 research outputs found
On topological structures of fuzzy parametrized soft sets
In this paper, we introduce the topological structure of fuzzy parametrized
soft sets and fuzzy parametrized soft mappings. We define the notion of
quasi-coincidence for fuzzy parametrized soft sets and investigated basic
properties of it. We study the closure, interior, base, continuity and
compactness and properties of these concepts in fuzzy parametrized soft
topological space
Spatial database implementation of fuzzy region connection calculus for analysing the relationship of diseases
Analyzing huge amounts of spatial data plays an important role in many
emerging analysis and decision-making domains such as healthcare, urban
planning, agriculture and so on. For extracting meaningful knowledge from
geographical data, the relationships between spatial data objects need to be
analyzed. An important class of such relationships are topological relations
like the connectedness or overlap between regions. While real-world
geographical regions such as lakes or forests do not have exact boundaries and
are fuzzy, most of the existing analysis methods neglect this inherent feature
of topological relations. In this paper, we propose a method for handling the
topological relations in spatial databases based on fuzzy region connection
calculus (RCC). The proposed method is implemented in PostGIS spatial database
and evaluated in analyzing the relationship of diseases as an important
application domain. We also used our fuzzy RCC implementation for fuzzification
of the skyline operator in spatial databases. The results of the evaluation
show that our method provides a more realistic view of spatial relationships
and gives more flexibility to the data analyst to extract meaningful and
accurate results in comparison with the existing methods.Comment: ICEE201
Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
Recent vigorous investigations of topological order have not only discovered
new topological states of matter but also shed new light to "already known"
topological states. One established example with topological order is the
valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are
disordered spin liquids with no spontaneous symmetry breaking but most
typically manifest topological order known as hidden string order on 1D chain.
Interestingly, the VBS models are based on mathematics analogous to fuzzy
geometry. We review applications of the mathematics of fuzzy super-geometry in
the construction of supersymmetric versions of VBS (SVBS) states, and give a
pedagogical introduction of SVBS models and their properties [arXiv:0809.4885,
1105.3529, 1210.0299]. As concrete examples, we present detail analysis of
supersymmetric versions of SU(2) and SO(5) VBS states, i.e. UOSp(N|2) and
UOSp(N|4) SVBS states whose mathematics are closely related to fuzzy two- and
four-superspheres. The SVBS states are physically interpreted as hole-doped VBS
states with superconducting property that interpolate various VBS states
depending on value of a hole-doping parameter. The parent Hamiltonians for SVBS
states are explicitly constructed, and their gapped excitations are derived
within the single-mode approximation on 1D SVBS chains. Prominent features of
the SVBS chains are discussed in detail, such as a generalized string order
parameter and entanglement spectra. It is realized that the entanglement
spectra are at least doubly degenerate regardless of the parity of bulk
(super)spins. Stability of topological phase with supersymmetry is discussed
with emphasis on its relation to particular edge (super)spin states.Comment: Review article, 1+104 pages, 37 figures, published versio
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