1,290 research outputs found
Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets. Volume II
The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; fuzzy measure; clustering algorithm; and many more
Interval-valued fuzzy graphs
We define the Cartesian product, composition, union and join on
interval-valued fuzzy graphs and investigate some of their properties. We also
introduce the notion of interval-valued fuzzy complete graphs and present some
properties of self complementary and self weak complementary interval-valued
fuzzy complete graphs
A representation theorem for quantale valued sup-algebras
With this paper we hope to contribute to the theory of quantales and
quantale-like structures. It considers the notion of -sup-algebra and shows
a representation theorem for such structures generalizing the well-known
representation theorems for quantales and sup-algebras. In addition, we present
some important properties of the category of -sup-algebras.Comment: 6 page
Covering rough sets based on neighborhoods: An approach without using neighborhoods
Rough set theory, a mathematical tool to deal with inexact or uncertain
knowledge in information systems, has originally described the indiscernibility
of elements by equivalence relations. Covering rough sets are a natural
extension of classical rough sets by relaxing the partitions arising from
equivalence relations to coverings. Recently, some topological concepts such as
neighborhood have been applied to covering rough sets. In this paper, we
further investigate the covering rough sets based on neighborhoods by
approximation operations. We show that the upper approximation based on
neighborhoods can be defined equivalently without using neighborhoods. To
analyze the coverings themselves, we introduce unary and composition operations
on coverings. A notion of homomorphismis provided to relate two covering
approximation spaces. We also examine the properties of approximations
preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin
Soft constraint abstraction based on semiring homomorphism
The semiring-based constraint satisfaction problems (semiring CSPs), proposed
by Bistarelli, Montanari and Rossi \cite{BMR97}, is a very general framework of
soft constraints. In this paper we propose an abstraction scheme for soft
constraints that uses semiring homomorphism. To find optimal solutions of the
concrete problem, the idea is, first working in the abstract problem and
finding its optimal solutions, then using them to solve the concrete problem.
In particular, we show that a mapping preserves optimal solutions if and only
if it is an order-reflecting semiring homomorphism. Moreover, for a semiring
homomorphism and a problem over , if is optimal in
, then there is an optimal solution of such that
has the same value as in .Comment: 18 pages, 1 figur
The moduli space of matroids
In the first part of the paper, we clarify the connections between several
algebraic objects appearing in matroid theory: both partial fields and
hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are
compatible with the respective matroid theories. Moreover, fuzzy rings are
ordered blueprints and lie in the intersection of tracts with ordered
blueprints; we call the objects of this intersection pastures.
In the second part, we construct moduli spaces for matroids over pastures. We
show that, for any non-empty finite set , the functor taking a pasture
to the set of isomorphism classes of rank- -matroids on is
representable by an ordered blue scheme , the moduli space of
rank- matroids on .
In the third part, we draw conclusions on matroid theory. A classical
rank- matroid on corresponds to a -valued point of
where is the Krasner hyperfield. Such a point defines a
residue pasture , which we call the universal pasture of . We show that
for every pasture , morphisms are canonically in bijection with
-matroid structures on .
An analogous weak universal pasture classifies weak -matroid
structures on . The unit group of can be canonically identified with
the Tutte group of . We call the sub-pasture of generated by
``cross-ratios' the foundation of ,. It parametrizes rescaling classes of
weak -matroid structures on , and its unit group is coincides with the
inner Tutte group of . We show that a matroid is regular if and only if
its foundation is the regular partial field, and a non-regular matroid is
binary if and only if its foundation is the field with two elements. This
yields a new proof of the fact that a matroid is regular if and only if it is
both binary and orientable.Comment: 83 page
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