Multiplexers are also called data selector.& de-multiplexer is called data distributer.MUX has multiple inputs & one output & that of de-multiplexer has one input & many outputs.MUX has n-inputs,m-select lines &1-output. De-multiplexer has 1-input,m-select lines & n-outputs.
An encoder changes the format of information from one form to another, for improving the speed and accuracy when transmitting, for keeping information securely, and for standardization. Encoder might reduce the effective storage size by converting the data into another format.
A decoder performs the opposite functions of the encoder, reversing the encoding process making converting the information to its previous format or other accessible format. For example, in electronics if a signal is encoded using an Analog to Digital Converter for transmission purposes the receiver has to decode the signal using Digital to Analog Converter to retrieve the original analog signal. In this case, ADC acts as the encoder and DAC act as the decoder.