Millis...alternate flash
You are trying to use millis() exactly like delay().  The method delay() stops the program from progressing forward.  It blocks the program.  This is frowned upon as the processor could be doing something useful during this time.  

The method millis() does not stop the program.  Instead it is like telling you what time it is.  It is your code that then need to know at what time you want to do something.  

But in your code, you are doing something odd.  You are switching the brightness of the LEDs then IMMEDIATELY switching them back.  You are using the same time for the two things you want to do.  Instead try to initialize previousMillisLED4 to 500, intervalLED3 to 1000 &amp; intervalLED4 to 1000.