The yellow fog that rubs its back upon the window-panes the yellow smoke that rubs its muzzle on the window-panes licked its tongue into the corners of the evening lingered upon the pools that stand in drains, let fall upon its back the soot that falls from chimneys, slipped by the terrace, made a sudden leap, and seeing that it was a soft october night curled once about the house, and fell asleep. in these lines, the poet metaphorically compares the fog to a rat a cat a blanket a prowler

a cat

The poem describes the fog as having a back it rubs on the window-panes. This immediately eliminates blanket as an option since the blanket doesn't have a back. Also, it later talks about the fog having a tongue, which a blanket does not have. It's also not a rat. A rat is often described with much more negative traits. The words "slipped" and "leap" are not usually descriptions for rats. A prowler also has a more negative connotation than what is portrayed in the poem. There is no indication that anything has been stolen. Also, at the end, the fog simply curls up and goes to sleep. It is much more peaceful than a prowler or rat would be.