A. Soltanpour‎‎ - Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, ‎Iran.‎
F. Baroughi‎‎ - Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, ‎Iran.‎
B. Alizadeh - Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, ‎Iran.

This paper investigates the p-center location problem on a network in which vertex weights and distances between vertices are uncertain. The concepts of the \alpha-p-center and the expected p-center are introduced. It is shown that the \alpha-p-center and the expected p-center models can be transformed into corresponding deterministic models. Finally, linear time algorithms for finding the ۱-center and \\۲-center of uncertain unweighted trees are ‎proposed.‎