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Not without knowing what's on the left side. Pull-up makes sense e.g. for 8051 port0, which has open drain outputs. In other cases, it may be waste of components and energy, respectively brainless copy-and-paste.
The pull-up resistor ensures that the wire is at a defined logic level even if no active devices are connected to it... It helps to maintain a logic state even if the input to the mux is disconnected suddenly and avoids error outputs... It actually maintains a state of logic High when input is inactive and an activeness of input will override the logic High state...
The pull-up resistors shouldn't be necessary if the microcontroller outputs are always either driven high or low.
However the pull-up resistors may be used to ensure that there is a logic level present at all times as demetal has said. This could be, as FvM has said, if the outputs are open-drain, or if they have mistakenly been configured as inputs or if the outputs are high-impedance tri-state, eg when the microcontroller is reset, etc.