The gradual rule inference mechanism consists in creating the optimal rule with linguistic approximations among linguistic terms of the linguistic variables of the gradual rule and facts base with degrees of similarity in a ad-hoc manner for the system.

For example, assume (resp. ) three fuzzy sets representing

• the linguistic values of the linguistic variable X (resp. Y) in the universe U (resp. V),
• the rule IF more X is THEN less Y is ,
• the fact X is .

The mechanism is the following (figure 6):

• do the linguistic approximation of in U :
• compute a fuzzy distance D between and :
• add D or subtract D to to obtain a new fuzzy sets .
• do the linguistic approximation of in V:
• apply the generalized modus ponens with the rule IF X is THEN Y is and the fact X is .

• Gradual Rules Optimization