Fuzzy Inference

A rule $b_k$ is a product (AND) of several Membership Functions $m{f}_j$ that can be active or not via the learnable parameter $p_{kj}$. $b_k(x)={\prod }_{j=1}^M{\left(m{f}_j(x)\right)}^{p_{kj}}=\exp \left({\sum }_{j=1}^M{p}_{kj}\ln \left(m{f}_j(x)\right)\right)$ The rewritten logarithmic form can be expressed as a Neural Network.