Penerapan Algoritma Floyd-Warshall pada Multigraf Fuzzy
DOI:
https://doi.org/10.25139/smj.v14i1.11515Abstract
Abstract
Essentially, a network is too complex to be described as a simple graph. Therefore, in real life, it can be represented as a multigraph with edge or vertex weights. However, the edge or vertex weights of a network may not be real-valued. This is because a system in a network can be built on fuzzy numbers. This article discusses the determination of optimal paths using a modified Floyd Warshall algorithm on fuzzy multigraphs. There are two main modifications made to the Floyd Warshall algorithm: eliminating duplicate edges in the first iteration and determining path weights using fuzzy numbers as a weight function. The interpretation of this optimal path is the path with the largest weight function. The results of the study show that the optimal path obtained based on fuzzy multigraphs provides a reliable solution to the problem discussed in this article.
Keywords: fuzzy graph; modified Floyd Warshall algorithm; network; optimal path
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