A Study of Fuzzy Minimum Spanning Trees Using Prufer Sequences
Keywords:
Fuzzy Minimum spanning tree problem, fuzzy number, Prufer sequencesAbstract
The fuzzy minimum spanning tree (FMST) problem, where the arc costs have fuzzy values, is one of the most studied problems in fuzzy sets and systems area. In this paper, we concentrate on an FMST problem on aPrufer sequence in which instead of a real number, is assigned to each arc length. The fuzzy Prufer sequences are able to represent the uncertainty in the arc costs of the fuzzy minimum spanning tree. Two key matters need to be addressed in FMST problem with fuzzy numbers. The other is how to determine the addition of edges to find out the cost of the FMST. The definite integration representation of fuzzy numbers is used here to solve these problems. A famous sequence to solve the minimum spanning tree problem is Prufer sequences, where uncertainty is not considered, i.e., specific values of arc lengths are provided. A fuzzy version of classical Prufer sequences is introduced in this paper to solve the FMST problem in the fuzzy environment. We use the concept of definite integration representation of the fuzzy numbers in the proposed algorithm
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