Risk Management for Fuzzy Random MST Problem Based on Conditional Value-at-Risk

This paper deals with a minimum spanning tree problem where each edge weight is a fuzzy random variable. In terms of risk management in order to avoid adverse impacts derived from uncertainty, conditional Value-at-Risk including a necessity measure for fuzziness is introduced as a risk measure. Furthermore, by performing the deterministic equivalent transformation, the proposed problem is transformed into an existing minimum spanning tree problem to apply polynomial-time algorithms, and a solution algorithm is developed to solve the proposed problem.