Chance constrained bottleneck spanning tree problem with fuzzy random edge costs

This paper considers a generalized fuzzy random version of bottleneck spanning tree problem in which edge costs are fuzzy random variables. The problem is to find an optimal spanning tree under chance constraint with respect to possibility measure of bottleneck (maximum cost) edge of spanning tree. The problem is first transformed into a deterministic equivalent problem. Then its subproblem is introduced and a close relation between these problems is clarified. Finally, fully utilizing this relation, we propose a polynomial order algorithm that finds an optimal spanning tree under two special functions.