Before revision:  We consider robust fault-tolerant k-center, matroid center and knapsack center, and develop pure or multi-criteria approximation algorithms for them. In order to address the fairness concern, we also consider variants of the aforementioned problems, namely fair robust fault-tolerant center problems.
After revision:  We consider robust fault-tolerant k-center, where each client is connected to multiple open facilities, thus having a vector of distances to these facilities, and the goal is to minimize the L_\infty norm of L_\infty norms of these vectors. In this paper, we study the maximum of norm problem. Given an arbitrary symmetric monotone norm f, the objective is defined as the maximum (L_\infty norm) of f-norm values of the induced cost vectors. This versatile formulation captures a wide variety of problems, including makespan minimization, fault-tolerant center problems.