Crisp and fuzzy categorisation

By Gordon Rugg

Categorisation occurs pretty much everywhere in human life. Most of the time, most of the categorisation appears so obvious that we don’t pay particular attention to it. Every once in a while, though, a case crops up which suddenly calls our assumptions about categorisation into question, and raises uncomfortable questions about whether there’s something fundamentally wrong in how we think about the world.

In this article, I’ll look at one important aspect of categorisation, namely the difference between crisp sets and fuzzy sets. It looks, and is, simple, but it has powerful and far-reaching implications for making sense of the world.

I’ll start with the example of whether or not you own a motorbike. At first glance, this looks like a straightforward question which divides people neatly into two groups, namely those who own motorbikes, and those who don’t. We can represent this visually as two boxes, with a crisp dividing line between them, like this.

However, when you’re dealing with real life, you encounter a surprising number of cases where the answer is unclear. Suppose, for instance, that someone has jointly bought a motorbike with their friend. Does that person count as being the owner of a motorbike, when they’re actually the joint owner? Or what about someone who has bought a motorbike on hire purchase, and has not yet finished the payments?

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