Javad Nematian - Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
Kuorosh Eshghi - Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

This paper investigates quadratic spanning tree problems where each cost attached to the edge and interactive cost between two edges in a given graph is represented with a fuzzy random variable. Fuzzy random quadratic minimum spanning tree problem is formulated by scalar expected value of fuzzy random variable and integer programming. The problem is to find optimal quadratic spanning tree that is based upon combination of Er-expected value of FRV and integer programming together with the B&B algorithm. An illustrative numerical example is given to clarify the theory and the method discussed in this paper.

Minimum spanning Tree, Fuzzy random variable, Expected value of FRV, Integer programming