This article explains two formats that use the MPLS file extension. It also explains how to open both types, and how to convert from that format to another.
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A file with the MPLS file extension may be a Blu-ray playlist. They are similar to MPL files and are typically saved with a five-digit filename, such as xxxxx.mpls, in the /bdmv/playlist/ directory on the disk.
The engineering mathematics software Mathcad may use the same file extension, but for font files.
If your MPLS file is a Blu-ray playlist, any Blu-ray player should be able to play the files contained within the file. Otherwise, you can try a program such as VLC, Media Player Classic Home Cinema (MPC-HC), JRiver Media Center, or CyberLink PowerDVD.