Weighted Fuzzy Production Rules
We suppose here that the fuzzy knowledge base is explained via the weighted fuzzy production rules or WFPR and the system modelling is realized via mapping these rules into an Adaptive Fuzzy Petri Nets.
Weighted Fuzzy Production Rules are categorized into three types as given below:
Assume that ai be the ith antecedent proposition of the rule, and c the consequent proposition.
All proposition ai can have the format "x is fa", where fa is the element of the sets of the fuzzy sets F.
Suppose λi be the threshold of the proposition to fire the rule.
Suppose wi be the weight of the antecedent ai.
Suppose μ be the certainty factor of the rule.
Then three categories of Weighted Fuzzy Production Rules are described as given below:
Type 1: A Simple Fuzzy Production Rule
R: IF a THEN c, λ, w (CF = μ)
For this type of rules as there are simply one proposition a in the antecedent, the weight w is 1 otherwise - 1.
Type 2: A Composed Conjunctive Rule
R: IF a1 AND a2 AND...AND an THEN c, λ1, λ2, λ3, w1, w2, ..., w3 (CF = μ).
Type 3: A Composed Disjunctive Rule.
R: IF a1 OR a2 OR ...OR an THEN c, λ1, λ2, λ3, w1, w2,..., w3 (CF = μ).