16,166 research outputs found
Arrow Index of Fuzzy Choice Function
The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality. Thus, if for solving a decision problem several fuzzy choice functions are proposed, by the Arrow index the most rational one will be chosen.Fuzzy choice function, revealed preference indicator, congruence indicator, similarity
Fuzzy Space-Time
A review is made of recent efforts to define linear connections and their
corresponding curvature within the context of noncommutative geometry. As an
application it is suggested that it is possible to identify the gravitational
field as a phenomenological manifestation of space-time commutation relations
and to thereby clarify its role as an ultraviolet regularizer.Comment: 17 pages LaTe
A genetic algorithm for the design of a fuzzy controller for active queue management
Active queue management (AQM) policies are those
policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the
hosts on the network borders, and the adoption of a suitable control
policy. This paper proposes the adoption of a fuzzy proportional
integral (FPI) controller as an active queue manager for Internet
routers. The analytical design of the proposed FPI controller is
carried out in analogy with a proportional integral (PI) controller,
which recently has been proposed for AQM. A genetic algorithm is
proposed for tuning of the FPI controller parameters with respect
to optimal disturbance rejection. In the paper the FPI controller
design metodology is described and the results of the comparison
with random early detection (RED), tail drop, and PI controller
are presented
Dirac Operators on Coset Spaces
The Dirac operator for a manifold Q, and its chirality operator when Q is
even dimensional, have a central role in noncommutative geometry. We
systematically develop the theory of this operator when Q=G/H, where G and H
are compact connected Lie groups and G is simple. An elementary discussion of
the differential geometric and bundle theoretic aspects of G/H, including its
projective modules and complex, Kaehler and Riemannian structures, is presented
for this purpose. An attractive feature of our approach is that it
transparently shows obstructions to spin- and spin_c-structures. When a
manifold is spin_c and not spin, U(1) gauge fields have to be introduced in a
particular way to define spinors. Likewise, for manifolds like SU(3)/SO(3),
which are not even spin_c, we show that SU(2) and higher rank gauge fields have
to be introduced to define spinors. This result has potential consequences for
string theories if such manifolds occur as D-branes. The spectra and
eigenstates of the Dirac operator on spheres S^n=SO(n+1)/SO(n), invariant under
SO(n+1), are explicitly found. Aspects of our work overlap with the earlier
research of Cahen et al..Comment: section on Riemannian structure improved, references adde
Consensus theories: an oriented survey
This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly â but not exclusively â concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de MathĂ©matique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity
Hyperbolic Supersymmetric Quantum Hall Effect
Developing a non-compact version of the SUSY Hopf map, we formulate the
quantum Hall effect on a super-hyperboloid. Based on group
theoretical methods, we first analyze the one-particle Landau problem, and
successively explore the many-body problem where Laughlin wavefunction,
hard-core pseudo-potential Hamiltonian and topological excitations are derived.
It is also shown that the fuzzy super-hyperboloid emerges in the lowest Landau
level.Comment: 14 pages, two columns, no figures, published version, typos correcte
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