Articles

Explanations that are meant to last longer than a blog post. For now they are all about one subject, fuzzy inference systems that learn from data, and about the two Python libraries I maintain for them.

Library	For	Built on
ANFIS Toolbox	classic ANFIS, small and medium problems	NumPy
highFIS	TSK systems for data with many features	PyTorch

The idea in one page

A Takagi-Sugeno-Kang (TSK) fuzzy system is a set of rules such as

if temperature is high and humidity is low then output is a linear function of the inputs

Words like high and low are fuzzy sets: instead of a hard threshold, each one has a membership function that says how much a value belongs to it, from 0 to 1. A rule fires as strongly as its conditions are true, and the answer of the system is the average of what every rule proposes, weighted by how strongly each one fired:

y = \sum_{r = 1}^{R} {\bar{w}}_{r} f_{r} (𝐱), {\bar{w}}_{r} = \frac{w_{r}}{\sum_{i = 1}^{R} w_{i}}

Two things make this more than an expert system. The shapes of the fuzzy sets and the coefficients of the rules can be learned from data, like the weights of a neural network. And after training the model is still a list of rules a person can read.

Reading order

How ANFIS works: the classic architecture, layer by layer
A first model with ANFIS Toolbox: from data to a trained model
Why fuzzy systems choke on many features: the problem highFIS exists to solve, with a demo you can run
The highFIS model families: a map of what is in the library