Coloring fuzzy graphs

Muñoz, S.; Ortuño, M.; Ramı́rez, Javier; Yáñez, Javier

doi:10.1016/j.omega.2004.04.006

Cited by 76 publications

(42 citation statements)

References 31 publications

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“…. , c À 1} if its color is C(i, j) = k. The coloring problem for fuzzy graphs has been studied by some authors (see [19]). And in order to color a fuzzy graph, we will consider the fuzzy edges that are greater than a prescribed threshold.…”

Section: The Coloring Problem For Fuzzy Graphsmentioning

confidence: 99%

A coloring fuzzy graph approach for image classification

Gómez

Montero

Yáñez

2006

Information Sciences

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Section: The Coloring Problem For Fuzzy Graphsmentioning

confidence: 99%

A coloring fuzzy graph approach for image classification

Gómez

Montero

Yáñez

2006

Information Sciences

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“…A teoria dos grafos é uma das áreas da programação matemática que tem utilizado frequentemente a teoria dos conjuntos fuzzy em alguns de seus problemas, dentre os quais se destacam: caminho mínimo [4][5][6][7][8][9][10][11], fluxo máximo [12][13][14][15], fluxo de custo mínimo [12,16,26], árvore geradora mínima [17][18][19][20][21] e coloração de grafos [22][23][24][25].…”

Section: Introductionunclassified

The Dominance Concept Applied in the Minimum Spanning Tree Problem with Fuzzy Parameters

Hernandes

Frighetto²,

Mulati³

2016

Revista Ciencias Exatas E Naturais

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Resumo: O problema da árvore geradora mínima com parâmetros fuzzy é um dos principais problemas da programação matemática fuzzy, visto que possui aplicações nas mais diversas áreas, como, por exemplo, redes de distribuição de energia, armazenamento de informações e transportes. Neste trabalho é proposto um algoritmo exato para o problema da árvore geradora mínima com estrutura crisp e parâmetros fuzzy. Trata-se de uma adaptação do algoritmo clássico de Prim, utilizando a relação de dominância de alguns trabalhos da literatura que tratam do problema de caminho mínimo fuzzy. As incertezas nos pesos são abordadas por meio da teoria dos conjuntos fuzzy e as árvores geradoras do conjunto solução são armazenadas usando o conceito de rótulos. O algoritmo proposto foi testado em três diferentes redes, compatíveis às instâncias dos principais trabalhos da literatura.

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“…Works on robustness in scheduling problem can be found in [9], [8], [4], [3]. Some works related to fuzzy graph coloring are there in [1], [6], [7], [5]. A work, somewhat similar to us, can be found in [9].…”

Section: Introductionmentioning

confidence: 99%

The Fuzzy Robust Graph Coloring Problem

Dey¹,

Pradhan

Pal

et al. 2015

Advances in Intelligent Systems and Computing

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Abstract. Fuzzy graph model can represent a complex, imprecise and uncertain problem, where classical graph model may fail. In this paper, we propose a fuzzy graph model to represent the examination scheduling problem of a university and introduce a genetic algorithm based method to find the robust solution of the scheduling problem that remains feasible and optimal or close to optimal for all scenarios of the input data. Fuzzy graph coloring method is used to compute the minimum number of days to schedule the examination. But problem arises if after the examination schedule is published, some students choose new courses in such a way that it makes the schedule invalid. We call this problem as fuzzy robust coloring problem (FRCP). We find the expression for robustness and based on its value, robust solution of the examination schedule is obtained. The concept of fuzzy probability of fuzzy event is used in the expression of robustness, which in turn, is used for fitness evaluation in genetic algorithm. Each chromosome in the genetic algorithm, used for FRCP, represents a coloring function. The validity of the coloring function is checked keeping the number of colors fixed. Fuzzy graphs with different number of nodes are used to show the effectiveness of the proposed method.

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Coloring fuzzy graphs

Cited by 76 publications

References 31 publications

A coloring fuzzy graph approach for image classification

A coloring fuzzy graph approach for image classification

The Dominance Concept Applied in the Minimum Spanning Tree Problem with Fuzzy Parameters

The Fuzzy Robust Graph Coloring Problem

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