Implement Multiplicative Fuzzy Logic
CJam, 45 bytes

q"-F"/"1 -"*"+F"/"1Y$-*+"*'F-S/)d\2/'\f*W%S*~


Uses precedence rule 6: strictly right-to-left. It expects ASCII input.

Take it for a spin!

Explanation

Read input, and perform the following transformations in order:

"-F"   to   "1 -"
"+F"   to   "1Y$-*+"
 "F"   to   ""


Then split over spaces (S/). Extract the rightmost element and convert it to a double ()d). Then take pairs from the rest of the list (\2/), join them all by \ ('\f*) and evaluate the resulting strings as CJam code in reverse order (W%S*~).

For example, it converts 5 +F 10 + 3


to 5 1Y$-*+ 10 + 3 in the first step,
then to 3 [["10" "+"] ["5" "1Y$-*+"]],
then to 3 ["10\+" "5\1Y$-*+"],
then to 3 10\+ 5\1Y$-*+, which is CJam code that computes the right answer, -47.