ABSTRACT
The fuzzy minimum spanning tree (FMST), which addresses the problem of optimizing networks, finds applications in many fields. Several types of algorithms are used to evaluate the minimum spanning tree (MST) when the environment is certain, but when the environment is uncertain, we use fuzzy parameters as vertices or edges. In the FMST, the vertices and arc lengths are defined in the form of a fuzzy number. In this research paper, we adopt new algorithmic schemes for obtaining FMST based on an acceptability index and a convex index, and then we verify our results using Yager's index. Here we consider a network with its vertices representing a fuzzy trapezoidal number. Finally, we evaluate the FMST of a given network and explain its detailed implementation with a numerical example.
