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:

Assumptions

Assume that a_i be the i^th antecedent proposition of the rule, and c the consequent proposition.

All proposition a_i can have the format "x is fa", where fa is the element of the sets of the fuzzy sets F.

Suppose λ_i be the threshold of the proposition to fire the rule.

Suppose w_i be the weight of the antecedent a_i.

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).