in crisp logic, the premise "x is a" can only be true or false. however, in a fuzzy rule, the premise "x is a" and the consequent "y is b" can be true to a degree, instead of entirely true or entirely false. this is achieved by representing the linguistic variables "a" and "b" using fuzzy sets. in a fuzzy rule, modus ponens is extended to "generalised modus ponens:."