We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decomposition's Dantzig-Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. The objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure.
Palavras-chave:Educação matemática. Conhecimentos prévios. Ensino fundamental.
Concepções de matemática.Resumo: Nesse artigo, apresentamos os resultados de uma investigação com abordagem quali-quantitativa, realizada com 22 estudantes de sexto ano do ensino fundamental de uma escola da rede pública de Tijucas, Santa Catarina, acerca do tema matemática. Para coleta de dados, foram usados registros escritos e os desenhos produzidos pelos estudantes. A análise de conteúdo a posteriori foi utilizada para interpretar os dados coletados, que constituíram tabelas e gráficos. Os resultados, de modo geral, mostram que os estudantes atribuem a concepção de matemática a fórmulas e à via utilitária, sua origem remonta à idade primitiva e um mundo sem matemática seria o caos.
Keywords:Mathematics education. Previous knowledge. Elementary school.
Conceptions of mathematics.Abstract: In this article, we presente the results about an investigation about an investigation with qualitative and quantitative approach, conducted with 22 students of the sixth grade of elementary school in a public school of Tijucas, Santa Catarina, about the mathematical topic. For data collection, written records and drawings produced by students were used. Subsequently the content analysis was used to interpret the data collected, which were tables and graphs. The results generally show that students assign the concept of mathematical formulas and utilitarian way, its origin dates back in the early age and a world without mathematics would be a chaos.
In this work we present two methods based in the classical Dantzig-Wolfe decomposition and a heuristic method, which solve problems with uncertainties in the parameters using the theory of fuzzy sets. The first one deals with uncertainties only in costs, while the others two deal with uncertainties in costs and restrictions. Methods using decomposition techniques address problems that have a special structure in the set of restrictions. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities that travel by the arcs of the network. The objective is to determine the flow of each commodity in the arcs, in order to meet demand at a minimal cost while respecting the capacity restrictions of the arcs and the flow conservation restrictions of the nodes. With the exception of the third, the other methods proposed in this work are not limited to solve fuzzy multicommodity flow problems, also solve fuzzy linear programming problems that have a special structure in a part of the set of restrictions.
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