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Conjonctive rules

There are two main families of conjunctive fuzzy rules:

  1. Mamdani type. The rule conclusion is a fuzzy set.
    The rule is written as:
    $\displaystyle IF \ x_1 \ is \ A_1^i \ AND \ x_2 \ is \ A_2^i \ \ldots \ AND \ x_p \ is \ A_p^i$      
    $\displaystyle THEN \ y_1 \ is \ C_1^i \ \ldots \ AND \ y_q \ is \ C_q^i$      

    where $ A_j^i \ and \ C_j^i$ are fuzzy sets defining the input and output space partitioning.


  2. Takagi-Sugeno type. The rule conclusion is a crisp value.
    The conclusion of the $ i_{th}$ rule for the $ j_{th}$ output is calculated as a linear function of the input values: $ y_j^i = b_{jo}^i + b_{j1}^i x_1 + b_{j2}^i x_2 + \cdots + b_{jp}^i x_p$ , also denoted $ y_j^i = f_j^i(x)$ .

    In FisPro, for interpretability reasons, the conclusion is limited to a constant $ b_{jo}^i$ .


next up previous contents
Next: Implicative rules Up: Fuzzy Logic Elementary Glossary Previous: Linguistic variable and fuzzy   Contents