A random fuzzy minimum spanning tree problem through a possibility-based value at risk model

This paper considers a minimum spanning tree problem under the situation where costs for constructing edges in a network include both fuzziness and randomness. In particular, this article focuses on the case that the edge costs are expressed by random fuzzy variables. A new decision making model based on a possibility measure and a value at risk measure is proposed in order to find a solution which fully reflects random and fuzzy information. It is shown that an optimal solution of the proposed model is obtained by a polynomial-time algorithm.

► A minimum spanning tree (MST) problem with random fuzzy edge costs is considered.
► New optimization criterion is constructed based on possibility and value at risk.
► The original problem is transformed into a deterministic nonlinear MST problem.
► An optimal solution of the transformed problem can be obtained in polynomial time.
► Note that a “random fuzzy” variable is different from a “fuzzy random” variable.