Dementia (from Latin de- "apart, away" + mens (genitive mentis) "mind") is the progressive decline in cognitive function due to damage or disease in the brain beyond what might be expected from normal aging. Although dementia is far more common in the geriatric population, it may occur in any stage of adulthood. This age cutoff is defining, as similar sets of symptoms due to organic brain dysfunction are given different names in populations younger than adulthood.
Alzheimer's is a form of dementia.
Unfortunately, I do not know the answer to your question, but an educated guess would be a smaller cruiseline. Smaller typically also means more expensive. Why would this person cruise alone?
Yeah, I assumed the OP meant dementia...and no, there is no "outfit" that caters to people with dementia. Of course, if you have a loved one that suffers from that there is nothing to stop you from taking them on a cruise with you if you feel that they will be all right onboard a ship, but you are still responsible for them.
You could look into hiring a companion (there are agencies that book private duty nurses and companions) to accompany such a person on a cruise - you might be able to negotiate a lower salary in exchange for the cruise fare, but not necessarily.