Visualization Algorithms for Multi-criteria Alternatives Filtering

Zakharova, Alena; Korostelyov, D.A.; Fedonin, Oleg

doi:10.26583/sv.11.4.06

Cited by 11 publications

(9 citation statements)

References 7 publications

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“…The geometric theory of multidimensional interpolation can also be used to solve other engineering problems of modeling and visualization multi-factor processes and phenomena [20][21][22][23][24][25][26][27][28][29][30].…”

Section: Resultsmentioning

confidence: 99%

About one method of numeral decision of differential equalizations in partials using geometric interpolants

Konopatskiy

Voronova

Бездитный

et al. 2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

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The article presents a new vision of the process of approximating the solution of differential equations based on the construction of geometric objects of multidimensional space incident to nodal points, called geometric interpolants, which have pre-defined differential characteristics corresponding to the original differential equation. The incidence condition for a geometric interpolant to nodal points is provided by a special way of constructing a tree of a geometric model obtained on the basis of the moving simplex method and using special arcs of algebraic curves obtained on the basis of Bernstein polynomials. A fundamental computational algorithm for solving differential equations based on geometric interpolants of multidimensional space is developed. It includes the choice and analytical description of the geometric interpolant, its coordinate-wise calculation and differentiation, the substitution of the values of the parameters of the nodal points and the solution of the system of linear algebraic equations. The proposed method is used as an example of solving the inhomogeneous heat equation with a linear Laplacian, for approximation of which a 16-point 2-parameter interpolant is used. The accuracy of the approximation was estimated using scientific visualization by superimposing the obtained surface on the surface of the reference solution obtained on the basis of the variable separation method. As a result, an almost complete coincidence of the approximation solution with the reference one was established.

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Section: Resultsmentioning

confidence: 99%

About one method of numeral decision of differential equalizations in partials using geometric interpolants

Konopatskiy

Voronova

Бездитный

et al. 2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

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show abstract

“…There are various methods for 2D imaging of single multi-criteria alternative [9]: Histograms, 2D plots, radar plots, radial plots, etc. The simplest method for visualizing many alternatives in three-dimensional space is to place two-dimensional images of alternatives along the 3rd coordinate axis ( Fig.…”

Section: Methods For Visualizing Multi-criteria Alternativesmentioning

confidence: 99%

Application of Visual Analytics Methods to Reduce the Dimensionality of Decision-making Problems

Zakharova¹,

Korostelyov²

2020

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The article discusses the possibilities and approaches to the use of visual analytics methods to reduce the dimension of decision-making problems. The main directions of reducing the dimension of the decision-making problem, as well as increasing its information content using three-dimensional visualization methods are highlighted: filtering alternatives, grouping and ranking criteria. The application of several methods of visualization of choice set and criteria set are considered: histograms with grouping by alternatives, histograms with grouping by criteria, correlation surfaces of criteria. The advantages and disadvantages of visualization methods are highlighted in relation to solving the problem of reducing the dimension of choice set and criteria set. The basic principles of increasing the efficiency of visual analytics of three-dimensional images for decision-making problem in order to reduce its dimension are noted. A description of an experiment on visual analytics of three-dimensional images is given on the example of the problem of choosing an optimal solver OpenFOAM (out of three alternatives) based on 24 results of computational experiments of supersonic flow around a cone with different initial parameters. It is noted that with the help of visual analytics, it was possible to find an error in one of the computational experiments, to reduce the number of alternatives to two, and the number of criteria to five, which made it possible to apply traditional decision-making methods to this problem and choose the optimal solver.

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“…However, the situation becomes more complicated if the number of components increases. In this case, the visibility of traditional approaches is greatly reduced and attempts are being made to develop new methods and approaches in this way [7]. Let's take another example.…”

Section: Practical Necessity Of Analysing the Dynamics Of Changes In mentioning

confidence: 99%

Visual Analysis of Dynamic Changes in Structured Data on the Basis of Colour Markers

Trubakova

Trubakov

2020

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One of the most important tasks for decision-making systems is obvious and intuitive visualization of input data. If they are displayed correctly and conveniently, this tool can become a very serious assistant for a decision-maker. Such a tool influences not only on the complexity of the decision-making process, but also the correctness and objectivity of the decisions made. Because of this so much attention is paid to this issue in various studies. However, nowadays the issue of displaying the dynamics of changes in structured data (data in which the observed value has an internal structure and consists of a large number of components) is not sufficiently developed. This paper focuses on these issues, provides a formal description of structured data, and suggests an approach to displaying the dynamics of their changes. The proposed approach to visualization allows to see both the general process of changing the observed value and the nature of changes in its internal structure. Separate charts give the opportunity to see the contribution of each component of a structured value and evaluate the dynamics of this contribution over time. The paper also shows the area of potential application of this approach, highlights its features and main prospects. Most of examples in the paper are based on the developed software package for modeling the situation with the spread of COVID-19 in Bryansk region, which used the proposed visualization option. There are also examples in which the proposed approach to visualization helps to get new information that is not visible when using other approaches to displaying structured data.

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Visualization Algorithms for Multi-criteria Alternatives Filtering

Cited by 11 publications

References 7 publications

About one method of numeral decision of differential equalizations in partials using geometric interpolants

About one method of numeral decision of differential equalizations in partials using geometric interpolants

Application of Visual Analytics Methods to Reduce the Dimensionality of Decision-making Problems

Visual Analysis of Dynamic Changes in Structured Data on the Basis of Colour Markers

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