When creating a rule base, if a rule has more than one antecedent, you must specify an antecedent connective to determine how to calculate the truth value of the aggregated rule antecedent.
Because linguistic variables can have partial degrees of membership within linguistic terms, you cannot use Boolean operators from conventional dual logic as antecedent connectives. PID and Fuzzy Logic VIs use the following antecedent connectives instead.
μA*B = min(μA, μB)
μA*B = (μA, μB)
μA + B = max(μA, μB)
A + B = ((A + B) - (AB))
Notice that these definitions agree with the logical operators used in Boolean logic. A truth table uses conventional operators to yield equivalent results.
The AND (Minimum) antecedent connective specifies to use the smallest degree of membership of the antecedents as the truth value of the aggregated rule antecedent, while the AND (Product) specifies to use the product of the degrees of membership of the antecedents. The OR (Maximum) antecedent connective specifies to use the largest degree of membership of the antecedents. The OR (Probabilistic) antecedent connective specifies to use the probabilistic sum of the degrees of membership of the antecedents.
Assume the following rules are invoked for the input values of a vehicle maneuvering fuzzy system.
| (1) | IF Vehicle Position x is Center (degree of membership = 0.8) |
AND (Minimum) | Vehicle Orientation β is Left Up (degree of membership = 1.0) = 0.8 |
| THEN Steering Angle φ is Negative Small | |||
| (2) | IF Vehicle Position x is Right Center (degree of membership = 0.1) |
AND (Minimum) | Vehicle Orientation β is Left Up (degree of membership = 1.0) = 0.1 |
| THEN Steering Angle φ is Negative Medium | |||
Notice that each rule uses the AND (Minimum) antecedent connective. In Rule 1, Vehicle Position x has a degree of membership of 0.8 within the linguistic term Center and Vehicle Orientation β has a degree of membership of 1.0 within the linguistic term Left Up. Because the antecedent connective is AND (Minimum), the fuzzy controller for this fuzzy system uses the smallest degree of membership of the antecedents, or 0.8, as the truth value of the aggregated rule antecedent. Similarly, the smallest degree of membership of the antecedents in Rule 2 is 0.1. Therefore, the fuzzy controller uses 0.1 as the truth value of the aggregated rule antecedent. The truth value of the aggregated rule antecedent is equivalent to the degree of truth of the rule.
If these two rules are the only rules invoked for a given set of input values, the other linguistic terms for the Steering Angle φ output linguistic variable have a truth value of 0. The following list describes the final truth values for each of the linguistic terms.
| Negative Large Negative Medium Negative Small Zero Positive Small Positive Medium Positive Large |
to a degree of to a degree of to a degree of to a degree of to a degree of to a degree of to a degree of |
�0.0 �0.1 �0.8 �0.0 �0.0 �0.0 �0.0 |
If a rule has more than one consequent, the fuzzy logic controller must evaluate the aggregated rule consequent. When you implement a fuzzy controller with PID and Fuzzy Logic VIs, the fuzzy controller always considers only the consequent that has the largest degree of membership.