This paper deals with interval state estimation for discrete-time Linear Parameter Varying (LPV) switched systems with the assumption that the dynamics of the measured polytopic parameters are described by a convex combination. The measurement noise and the state disturbance are assumed to be unknown but bounded. The switching signal is supposed to be known among system modes. By adopting Multiple Quadratic Lyapunov Functions (MQLF) and Average Dwell Time (ADT) concept, new and less conservative cooperativity and Input to State Stability (ISS) conditions are derived and expressed on the vertices of each polytope in order to avoid any infinite dimensional problem due to the time varying measured parameters. Finally, a numerical example shows the efficiency of the proposed interval observer.