14,898 research outputs found
Aggregating fuzzy subgroups and T-vague groups
Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations).
In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft
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
Relations on FP-Soft Sets Applied to Decision Making Problems
In this work, we first define relations on the fuzzy parametrized soft sets
and study their properties. We also give a decision making method based on
these relations. In approximate reasoning, relations on the fuzzy parametrized
soft sets have shown to be of a primordial importance. Finally, the method is
successfully applied to a problems that contain uncertainties.Comment: soft application
Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors
We review our construction of a bifundamental version of the fuzzy 2-sphere
and its relation to fuzzy Killing spinors, first obtained in the context of the
ABJM membrane model. This is shown to be completely equivalent to the usual
(adjoint) fuzzy sphere. We discuss the mathematical details of the
bifundamental fuzzy sphere and its field theory expansion in a
model-independent way. We also examine how this new formulation affects the
twisting of the fields, when comparing the field theory on the fuzzy sphere
background with the compactification of the 'deconstructed' (higher
dimensional) field theory.Comment: Invited contribution to special issue of SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) "Noncommutative Spaces
and Fields
Monopole Bundles over Fuzzy Complex Projective Spaces
We give a construction of the monopole bundles over fuzzy complex projective
spaces as projective modules. The corresponding Chern classes are calculated.
They reduce to the monopole charges in the N -> infinity limit, where N labels
the representation of the fuzzy algebra.Comment: 30 pages, LaTeX, published version; extended discussion on asymptotic
Chern number
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