Is it possible that a human being have red or violet eyes ?

I guess: If you mean the white part of the eye, then yes. If the sclera, episclera or conjunctiva get sufficiently irritated or inflamed, they can look red--even violaceous. If you mean the colored part of the eye, well, i suppose it could if the eye was filled with blood (and even that would look closer to brown or black) or they had albinism (they would be pink from lack of pigment).

Violet maybe, no red: Iris can be many colors and some have a mixture of blue and other colors that look sort of violet - think of Elizabeth Taylor. Red is only possible if the iris surface is covered with blood vessels which is not normal but pathologic. Some advanced albinos have pink eyes.