This is likely to be because your control chain is catching the edge of the fabric when opening and closing your blind. This will be due to one of two reasons.

Firstly, you could be pulling the control chain at an angle across the fabric, possibly due to an obstruction such as curtains which overhang the outside of your window. If this is the reason, ensure that the chain is pulled directly away from the window, ensuring that it doesn’t catch on the fabric.

Secondly, it could be because your fabric is running off, probably because the surface that your blind is fitted to is slightly uneven. 

If this is the case, refit the blind so that it is level, roll the blind down and then back up to the top again.Assuming that you can rectify the reason for the fraying then carefully trim any stray threads with a sharp pair of scissors and ensure the blind is operated correctly.