Traditional multi-criteria decision making (MCDM) algorithms are used in the handover of user equipment (UE) in an Ultra Dense Network (UDN). UDN refers to the increased density of the Radio Access Technologies (RATs) in a region which leads to the overlapping of the areas covered by individual RATs. MCDM algorithms such as TOPSIS, PROMETHEE and SAW are used to initiate handovers between these RATs based on the parameters obtained by the UE from each of the overlapping networks. However, initiating a handover abruptly and frequently, in case of availability of a new RAT without any thresholding technique proves to be unfriendly to the system resources. This can degrade the performance of the system. In this paper, a thresholding approach to the handover procedure is integrated to the MCDM process for the selection of RATs. First, an application-specific approach has been used in the selection of weights using the analytical hierarchy process which, is depending upon the application being used by the user. Then the ranking of the available RATs is done using the various MCDM algorithms and depending on the threshold specified for a handover, a decision is made whether to perform the handover process or not. In the case of streaming class of network traffic, the proposed method improves the performance of the system and reduces the handover by 13.14%, 19.35% and 8.62% of RAT modifications for TOPSIS, PROMETHEE and SAW respectively.