When facing a knife fighter whose strength comes from having the knife, if you attack the person, he or she will try to protect the knife from your attack and then counter with slashes, rather than worrying about protecting his or her brain. So, to defend against a knife fighter, attack his or her brain.
This may be accomplished through many means, but one proven approach is first to close the range quickly. If you stand away from the attacker, you will be constantly on the defensive, dodging slashing attacks and not attacking. You need to get close so you may attack the attacker's central nervous system. Your weapons of choice are your forearms, since they are hard, versatile, and, unlike the hands, they may take punishment without serious injury. As you rush in, attack with downward, circular strikes, flailing your forearms inward in a flurry of attacks similar to two propellers beating on the attacker. Do not reach out with the arms, keep them in close for power and to permit quicker follow-up attacks. This type of attack provides protection to your torso and generates powerful strikes that overwhelm the attacker. The attacker never gets to think about anything, including using the knife.
The forearm attacks are aimed to strike multiple targets. The first strikes are to the attacker's arms and then they rapidly advance upward. When you reach the neck, you will find yourself well inside the attacker's defenses, with access to the attacker's central nervous system. Focus the forearms strikes to crush the windpipe, strike the vagus nerve that runs vertically along each side of the neck, the temples, the nose, the ears, and the jaw hinges. Use your thumbs to gouge the eyes. One of these attacks will incapacitate the attacker, and the knife will no longer be a problem. You will probably get cut during the attacks, but the attacker will be fighting for his or her life and will not be making effective knife strokes. You will be bleeding, but you will heal; whereas, your attacker will be dead or unconscious.
When facing a knife attack, focus on attacking your attacker, not on defending against a slashing attack. You will get cut, but you will win. It is highly unlikely you will ever be attacked by a trained fighter with a knife. It is more likely you will be attacked by an idiot who is used to having everyone cower and be intimidated by his or her knife. They will have no defenses against your vicious attack that ignores their knife.