Search results for "Computational Mathematics"
showing 10 items of 986 documents
Consistent Clustering of Elements in Large Pairwise Comparison Matrices
2018
[EN] In multi-attribute decision making the number of decision elements under consideration may be huge, especially for complex, real-world problems. Typically these elements are clustered and then the clusters organized hierarchically to reduce the number of elements to be simultaneously handled. These decomposition methodologies are intended to bring the problem within the cognitive ability of decision makers. However, such methodologies have disadvantages, and it may happen that such a priori clustering is not clear, and/or the problem has previously been addressed without any grouping action. This is the situation for the case study we address, in which a panel of experts gives opinions…
A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations
2019
Abstract In this paper we show a strategy to devise third order iterative methods based on classic second order ones such as Steffensen’s and Kurchatov’s. These methods do not require the evaluation of derivatives, as opposed to Newton or other well known third order methods such as Halley or Chebyshev. Some theoretical results on convergence will be stated, and illustrated through examples. These methods are useful when the functions are not regular or the evaluation of their derivatives is costly. Furthermore, special features as stability, laterality (asymmetry) and other properties can be addressed by choosing adequate nodes in the design of the methods.
Formal ontology and CAD integration with macro parametric approach
2017
ABSTRACTThis paper discusses an ontological integration framework in the context of mereotopological formal ontology and CAD systems. Based on a comprehensive literature review of current design knowledge management and formal ontology research works, the authors propose the integration framework that can incorporate design knowledge with CAD systems. The primary role of mereotopology in this research work is the formal representation of design knowledge for the 3D solid assembly models. Most of the existing research works about design ontology present an abstract form and often require significant additional efforts to be integrated into CAD systems. Thus, this work introduces a formal ont…
Modeling and control of uncertain nonlinear systems
2018
A survey of the methodologies associated with the modeling and control of uncertain nonlinear systems has been given due importance in this paper. The basic criteria that highlights the work is relied on the various patterns of techniques incorporated for the solutions of fuzzy equations that corresponds to fuzzy controllability subject. The solutions which are generated by these equations are considered to be the controllers. Currently, numerical techniques have come out as superior techniques in order to solve these types of problems. The implementation of neural networks technique is contributed in the complex way of dealing the appropriate coefficients and solutions of the fuzzy systems.
Intelligent agents for feature modelling in computer aided design
2017
Abstract CAD modelling can be referred to as the process of generating an integrated multiple view model as a representation of multiple views of engineering design. In many situations, a change in the model of one view may conflict with the models of other views. In such situations, the model of some views needs to be adapted in order to make all models consistent. Thus, CAD models should be capable of adapting themselves to new situations. Recently, agent based technologies have been considered in order to increase both knowledge level and intelligence of real and virtual objects. The contribution of this paper consists in introducing the intelligent agents in intelligent CAD modelling. T…
Fuzzy Modeling for Uncertain Nonlinear Systems Using Fuzzy Equations and Z-Numbers
2018
In this paper, the uncertainty property is represented by Z-number as the coefficients and variables of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. Here, we use fuzzy equations as the models for the uncertain nonlinear systems. The modeling of the uncertain nonlinear systems is to find the coefficients of the fuzzy equation. However, it is very difficult to obtain Z-number coefficients of the fuzzy equations.
A singular elliptic equation and a related functional
2021
We study a class of Dirichlet boundary value problems whose prototype is [see formula in PDF] where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on [see formula in PDF] whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
Graph-theoretical derivation of brain structural connectivity
2020
Brain connectivity at the single neuron level can provide fundamental insights into how information is integrated and propagated within and between brain regions. However, it is almost impossible to adequately study this problem experimentally and, despite intense efforts in the field, no mathematical description has been obtained so far. Here, we present a mathematical framework based on a graph-theoretical approach that, starting from experimental data obtained from a few small subsets of neurons, can quantitatively explain and predict the corresponding full network properties. This model also changes the paradigm with which large-scale model networks can be built, from using probabilisti…
Comparing interactive evolutionary multiobjective optimization methods with an artificial decision maker
2021
AbstractSolving multiobjective optimization problems with interactive methods enables a decision maker with domain expertise to direct the search for the most preferred trade-offs with preference information and learn about the problem. There are different interactive methods, and it is important to compare them and find the best-suited one for solving the problem in question. Comparisons with real decision makers are expensive, and artificial decision makers (ADMs) have been proposed to simulate humans in basic testing before involving real decision makers. Existing ADMs only consider one type of preference information. In this paper, we propose ADM-II, which is tailored to assess several …
Variable neighborhood descent for the incremental graph drawing
2017
Abstract Graphs are used to represent reality in several areas of knowledge. Drawings of graphs have many applications, from project scheduling to software diagrams. The main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion for a good representation of a graph. In this paper we target the edge crossing reduction in the context of incremental graph drawing, in which we want to preserve the layout of a graph over successive drawings. We propose a hybrid method based on the GRASP (Greedy Randomized Adaptive Search Procedure) and VND (Variable Neighborhood Descent) methodologies and compare it with previous methods via simulation.