en Fuzzy Sets and Systems Fuzzy Sets and Systems پژوهشی Original The backup 2-median location problem on a tree T is to deploy two servers at the vertices such that the expected sum of distances from all vertices to the set of functioning servers is minimum. In this paper, we investigate the backup 2-median location problem on tree networks with trapezoidal interval type-2 fuzzy weights. We first, present  a new  method for comparing generalized trapezoidal fuzzy numbers and then develop it for trapezoidal interval type-2 fuzzy numbers. Then numerical examples are given to compare the proposed methods with other existing  methods. Finally, we apply our ranking method to  solve the the backup 2-median location problem on a tree network with trapezoidal interval type-2 fuzzy weights. Location theory, Backup 2-median, Generalized fuzzy number, Trapezoidal interval type-2 fuzzy number 133 148 http://iors.ir/journal/browse.php?a_code=A-10-1582-2&slc_lang=en&sid=1 Sepideh Taghikhani staghikhani234@gmail.com 00031947532846002954 00031947532846002954 No Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran Fahimeh Baroughi baroughi@sut.ac.ir 00031947532846002955 00031947532846002955 Yes Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran Behrooz Alizadeh alizadeh@sut.ac.ir 00031947532846002956 00031947532846002956 No Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran