The Mediterranean diet has long been linked to lower rates of dementia. Olive oil, a staple of the traditional Mediterranean diet, is rich in monounsaturated fatty acid (oleic acid, specifically). The Mediterranean diet is also relatively low in saturated fatty acid.
From a 2012 study done by Harvard researchers:
“In conclusion, these data suggest that elevated saturated fatty acid intake is related to worse late-life cognitive trajectory, and increased monounsaturated fatty acid intake is related to better cognitive aging. Thus, decreasing saturated fatty acid and increasing monounsaturated fatty acid merit further consideration in promoting healthy cognitive aging, and dietary patterns that incorporate higher intake of “good” fats (e.g., Mediterranean) should be further addressed in cognitive aging research.”
Source: Dietary fat types and 4-year cognitive change in community-dwelling older women
PS: The study at hand involved women, so results may not apply to older men.