8,743 research outputs found
Logarithmic aggregation operators and distance measures
The Hamming distance is a well‐known measure that is designed to provide insights into the similarity between two strings of information. In this study, we use the Hamming distance, the optimal deviation model, and the generalized ordered weighted logarithmic averaging (GOWLA) operator to develop the ordered weighted logarithmic averaging distance (OWLAD) operator and the generalized ordered weighted logarithmic averaging distance (GOWLAD) operator. The main advantage of these operators is the possibility of modeling a wider range of complex representations of problems under the assumption of an ideal possibility. We study the main properties, alternative formulations, and families of the proposed operators. We analyze multiple classical measures to characterize the weighting vector and propose alternatives to deal with the logarithmic properties of the operators. Furthermore, we present generalizations of the operators, which are obtained by studying their weighting vectors and the lambda parameter. Finally, an illustrative example regarding innovation project management measurement is proposed, in which a multi‐expert analysis and several of the newly introduced operators are utilized
Induced and logarithmic distances with multi-region aggregation operators
Copyright © 2019 The Author(s). Published by VGTU Press. This paper introduces the induced ordered weighted logarithmic averaging IOWLAD and multiregion induced ordered weighted logarithmic averaging MR-IOWLAD operators. The distinctive characteristic of these operators lies in the notion of distance measures combined with the complex reordering mechanism of inducing variables and the properties of the logarithmic averaging operators. The main advantage of MR-IOWLAD operators is their design, which is specifically thought to aid in decision-making when a set of diverse regions with different properties must be considered. Moreover, the induced weighting vector and the distance measure mechanisms of the operator allow for the wider modeling of problems, including heterogeneous information and the complex attitudinal character of experts, when aiming for an ideal scenario. Along with analyzing the main properties of the IOWLAD operators, their families and specific cases, we also introduce some extensions, such as the induced generalized ordered weighted averaging IGOWLAD operator and Choquet integrals. We present the induced Choquet logarithmic distance averaging ICLD operator and the generalized induced Choquet logarithmic distance averaging IGCLD operator. Finally, an illustrative example is proposed, including real-world information retrieved from the United Nations World Statistics for global regions
Group-decision making with induced ordered weighted logarithmic aggregation operators
This paper presents the induced generalized ordered weighted logarithmic aggregation (IGOWLA) operator, this operator is an extension of the generalized ordered weighted logarithmic aggregation (GOWLA) operator. It uses order-induced variables that modify the reordering process of the arguments included in the aggregation. The principal advantage of the introduced induced mechanism is the consideration of highly complex attitude from the decision makers. We study some families of the IGOWLA operator as measures for the characterization of the weighting vector (...
The regularity of the boundary of a multidimensional aggregation patch
Let and let be the fundamental solution of the Laplace
equation in We consider the aggregation equation with
initial data , where is the indicator
function of a bounded domain We now fix and
take to be a bounded domain (a domain with smooth boundary
of class ). Then we have Theorem: If is a
domain, then the initial value problem above has a solution given by
where is a domain for all
Stochastic suspensions of heavy particles
Turbulent suspensions of heavy particles in incompressible flows have gained
much attention in recent years. A large amount of work focused on the impact
that the inertia and the dissipative dynamics of the particles have on their
dynamical and statistical properties. Substantial progress followed from the
study of suspensions in model flows which, although much simpler, reproduce
most of the important mechanisms observed in real turbulence. This paper
presents recent developments made on the relative motion of a pair of particles
suspended in time-uncorrelated and spatially self-similar Gaussian flows. This
review is complemented by new results. By introducing a time-dependent Stokes
number, it is demonstrated that inertial particle relative dispersion recovers
asymptotically Richardson's diffusion associated to simple tracers. A
perturbative (homogeneization) technique is used in the small-Stokes-number
asymptotics and leads to interpreting first-order corrections to tracer
dynamics in terms of an effective drift. This expansion implies that the
correlation dimension deficit behaves linearly as a function of the Stokes
number. The validity and the accuracy of this prediction is confirmed by
numerical simulations.Comment: 15 pages, 12 figure
Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure
We analyse the asymptotic behaviour of solutions to the one dimensional
fractional version of the porous medium equation introduced by Caffarelli and
V\'azquez, where the pressure is obtained as a Riesz potential associated to
the density. We take advantage of the displacement convexity of the Riesz
potential in one dimension to show a functional inequality involving the
entropy, entropy dissipation, and the Euclidean transport distance. An argument
by approximation shows that this functional inequality is enough to deduce the
exponential convergence of solutions in self-similar variables to the unique
steady states
The abelian sandpile and related models
The Abelian sandpile model is the simplest analytically tractable model of
self-organized criticality. This paper presents a brief review of known results
about the model. The abelian group structure allows an exact calculation of
many of its properties. In particular, one can calculate all the critical
exponents for the directed model in all dimensions. For the undirected case,
the model is related to q= 0 Potts model. This enables exact calculation of
some exponents in two dimensions, and there are some conjectures about others.
We also discuss a generalization of the model to a network of communicating
reactive processors. This includes sandpile models with stochastic toppling
rules as a special case. We also consider a non-abelian stochastic variant,
which lies in a different universality class, related to directed percolation.Comment: Typos and minor errors fixed and some references adde
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