As Transistor has answered, your best bet is to make 4 independent window conparators. If you are determined to do things the hard way, the following
simulate this circuit – Schematic created using CircuitLab
actually makes use of the 74147 as a priority encoder. Unfortunately, what you want is a dot-mode bar graph, and the 147 doesn't do that. You can, however, add a 2:4 demultiplexer (I've used half the inputs of a 3:8, just because it's convenient) to convert the encoded address to drive the LEDs.
Additionally, LM339s have as much as 3 mV offsets, and although you expect the 4 on a chip to track with temperature, the unit-to-unit offset is not correlated on a chip. This means that your LEDs 2 and 3, which have windows less than 10 mV wide, will potentially have 30% errors on each end of the windows. To get around this, I've added a front end which converts (0.118 to 0.1999) to (0.1 to 3.1) volts. The two op amps should be rail-to-rail output units capable of running at 5 volts. The choice of 3.1 volts as an upper limit comes from the LM339 common mode input limits of 0 to 3.5 volts for a 5 volt supply.
Also note that the accuracy of the windows depends critically on the accuracy of the 5 volt supply. Any variations will directly impact the thresholds of the windows.
Finally, my suggested circuit needs, and does not have, hysteresis. However, I don't know your threshold accuracy requirement nor did you specify the amount of noise which may be found on the input. Without these, there is no way to specify what's needed.