238 research outputs found
On Generalised Interval-Valued Fuzzy Soft Sets
Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for
dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of
generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The
lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an
application of the new approach in decision making based on generalised interval-valued fuzzy
soft set is developed
Four-fold Formal Concept Analysis based on Complete Idempotent Semifields
Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two powersets. In this paper we extend the FCA formalism to include all four Galois connections between four different semivectors spaces over idempotent semifields, at the same time. The result is K¯¯¯¯-four-fold Formal Concept Analysis (K¯¯¯¯-4FCA) where K¯¯¯¯ is the idempotent semifield biasing the analysis. Since complete idempotent semifields come in dually-ordered pairs—e.g., the complete max-plus and min-plus semirings—the basic construction shows dual-order-, row–column- and Galois-connection-induced dualities that appear simultaneously a number of times to provide the full spectrum of variability. Our results lead to a fundamental theorem of K¯¯¯¯-four-fold Formal Concept Analysis that properly defines quadrilattices as 4-tuples of (order-dually) isomorphic lattices of vectors and discuss its relevance vis-à-vis previous formal conceptual analyses and some affordances of their results
Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain
As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied
Upscaling and spatial localization of non-local energies with applications to crystal plasticity
We describe multiscale geometrical changes via structured deformations (g, G) and the non-local energetic response
at a point x via a function 9 of the weighted averages of the jumps [un](y) of microlevel deformations un at points y
within a distance r of x. The deformations un are chosen so that limn→∞ un = g and limn→∞ ∇un = G. We provide
conditions on 9 under which the upscaling “n → ∞” results in a macroscale energy that depends through 9 on (1)
the jumps [g] of g and the “disarrangement field” ∇g − G, (2) the “horizon” r, and (3) the weighting function αr
for
microlevel averaging of [un](y). We also study the upscaling “n → ∞” followed by spatial localization “r → 0” and
show that this succession of processes results in a purely local macroscale energy I(g, G) that depends through 9
upon the jumps [g] of g and the “disarrangement field” ∇g − G alone. In special settings, such macroscale energies
I(g, G) have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader
setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity
of single crystals
Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots
Most scientific challenges can be framed into one of the following three
levels of complexity of function approximation. Type 1: Approximate an unknown
function given input/output data. Type 2: Consider a collection of variables
and functions, some of which are unknown, indexed by the nodes and hyperedges
of a hypergraph (a generalized graph where edges can connect more than two
vertices). Given partial observations of the variables of the hypergraph
(satisfying the functional dependencies imposed by its structure), approximate
all the unobserved variables and unknown functions. Type 3: Expanding on Type
2, if the hypergraph structure itself is unknown, use partial observations of
the variables of the hypergraph to discover its structure and approximate its
unknown functions. While most Computational Science and Engineering and
Scientific Machine Learning challenges can be framed as Type 1 and Type 2
problems, many scientific problems can only be categorized as Type 3. Despite
their prevalence, these Type 3 challenges have been largely overlooked due to
their inherent complexity. Although Gaussian Process (GP) methods are sometimes
perceived as well-founded but old technology limited to Type 1 curve fitting,
their scope has recently been expanded to Type 2 problems. In this paper, we
introduce an interpretable GP framework for Type 3 problems, targeting the
data-driven discovery and completion of computational hypergraphs. Our approach
is based on a kernel generalization of Row Echelon Form reduction from linear
systems to nonlinear ones and variance-based analysis. Here, variables are
linked via GPs and those contributing to the highest data variance unveil the
hypergraph's structure. We illustrate the scope and efficiency of the proposed
approach with applications to (algebraic) equation discovery, network discovery
(gene pathways, chemical, and mechanical) and raw data analysis.Comment: The code for the algorithm introduced in this paper and its
application to various examples are available for download (and as as an
installable python library/package) at
https://github.com/TheoBourdais/ComputationalHypergraphDiscover
K-Formal Concept Analysis as linear algebra over idempotent semifields
We report on progress in characterizing K-valued FCA in algebraic terms, where K is an idempotent semifield. In this data mining-inspired approach, incidences are matrices and sets of objects and attributes are vectors. The algebraization allows us to write matrix-calculus formulae describing the polars and the fixpoint equations for extents and intents. Adopting also the point of view of the theory of linear operators between vector spaces we explore the similarities and differences of the idempotent semimodules of extents and intents with the subspaces related to a linear operator in standard algebra. This allows us to shed some light into Formal Concept Analysis from the point of view of the theory of linear operators over idempotent semimodules.
In the opposite direction, we state the importance of FCA-related concepts for dual order homomorphisms of linear spaces over idempotent semifields, specially congruences, the lattices of extents, intents and formal concepts
Alternatives for jet engine control
The development of models of tensor type for a digital simulation of the quiet, clean safe engine (QCSE) gas turbine engine; the extension, to nonlinear multivariate control system design, of the concepts of total synthesis which trace their roots back to certain early investigations under this grant; the role of series descriptions as they relate to questions of scheduling in the control of gas turbine engines; the development of computer-aided design software for tensor modeling calculations; further enhancement of the softwares for linear total synthesis, mentioned above; and calculation of the first known examples using tensors for nonlinear feedback control are discussed
The Encyclopedia of Neutrosophic Researchers - vol. 1
This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements
A survey of congruences and quotients of partially ordered sets
The literature on congruences and quotients of partially ordered sets contains a large and profilerating array of approaches, but little in the way of systematic exposition and examination of the subject. We seek to rectify this by surveying the different approaches in the literature and providing philosophical discussion on requirements for notions of congruences of posets. We advocate a pluralist approach which recognises that different types of congruence arise naturally in different mathematical situations. There are some notions of congruence which are very general, whilst others capture specific structure which often appears in examples. Indeed, we finish by giving several examples where quotients of posets appear naturally in mathematics
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