Abstract
Abstract In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem. Costs of all the edges are considered as fuzzy numbers. Using the m λ measure, a generalization of credibility measure, the problem is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prufer like code representation of labeled trees.
Highlights
The minimum spanning tree (MST) problem is one of the fundamental problems in graph theory
Gao and Lu20 proposed the concepts of expected minimum spanning tree (EMST), α-pessimistic minimum spanning tree (α-PMST) and most minimum spanning tree (MMST) in a fuzzy quadratic minimum spanning tree (FQMST) problem, based on the credibility theory. They discussed the crisp equivalent problems when the fuzzy costs are characterized by trapezoidal fuzzy numbers and devised genetic algorithm to solve those
We propose the α-PMST and MMST models of the diameter constrained fuzzy minimum spanning tree (DCFMST) problem, based on the mλ measure
Summary
The minimum spanning tree (MST) problem is one of the fundamental problems in graph theory. Let G = (V, E) be a finite undirected simple connected graph with a set V of vertices and a set E of edges. A tree T with the same vertex set V is called a spanning tree of G. Suppose a positive weight wi is associated with every edge ei in G. W(T ) = ∑ wi ei∈T is called the weight of the spanning tree T. The MST problem is to find a spanning tree T ∗ from the set Γ of all spanning trees of G such that w(T ∗) =
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