I know you are confused and asking ” What are hair hats?”. The answer is simple ” Bad Wigs”. Wigs that are soooooooo noticeable ( too long, bulky etc.) they appear to be hats on both men and women’s head.
If you have this problem, there is a simple hair tool that can help you. This tool is called a Thinning Shear. Thinning Shears are unique in look and function. It is comprised of one full blade and one cerated blade that resembles a comb. The shears composition aids in its special function of thinning out hair. You will not cut down the length of the hair style as in using regular scissors or razors but lessen the volume gradually.
Here are som tips for Wig Thinning:
1) Never thin out wigs by the hairline.
2) Never thin out hair on the top crown.
3) Try not to over thin one area.
4) Take your time when thinning, you don’t want to have to purchase wigs frequently.
Women's Hair Loss 
Thanks for the advice, my Dad was a barber, I know he thined hair with this tool, I was hoping you could use it on wigs to. My Paula Young wigs, are beautiful, and look so real, but they are to full on the sides and back for my head. This should be the answer to my problem, Thanks again