Mean–variance value at risk criterion for solving a p-median location problem on networks with type-2 intuitionistic fuzzy weights

Abstract

In this paper, we consider the p-median location problem on networks in which the vertex weights are the type-2 intuitionistic fuzzy variables. First, the credibilistic value at risk of the intuitionistic fuzzy variables is introduced. Using value at risk criterion, we define a new method for reducing of type-2 intuitionistic fuzzy variables to intuitionistic fuzzy variables that is named the value at risk reduced intuitionistic fuzzy variables. Further, the mean and variance values of value at risk reduced intuitionistic fuzzy variables are described. Finally, we apply the mean–variance criterion for solving the type-2 intuitionistic fuzzy p-median location problem. Also, it is shown that this problem is equivalent to a parametric quadratic convex programming problem.