The Fuzzy Set Theory of Startups

Or yet another mental model for thinking about the future

About a year and a half ago, I wrote a piece titled “Square Pegs Don’t Fit in Round Holes,” where I discussed business model — problem fit. In retrospect, the piece is pretty simplistic, but it gets at a point I still can’t stop thinking about.

The Original Logic

Here’s what I originally conceived with business model — problem fit. There are potentially hundreds (or even thousands) of unique business models that companies could incorporate. Each business model and problem space have a unique set of n features, and for the startups that succeed, the feature set of the business model maps accordingly onto the feature set of the problem space or opportunity area being tackled. Here’s a high-level visual illustration with Uber, a company people know.

In a perfect world, you know exactly what constitutes the feature set of the business model and the problem area. But, the world is far from perfect.

Enter Fuzzy Set Theory

Even though models are supposed to be generalizable, the idea I initially proposed felt too abstract. That’s where fuzzy sets, a branch within mathematics and set theory (the study of collections of objects), come in. I’ll preface this by saying this explanation keeps things very high level but I believe there are some interesting takeaways from the theory.

Within classical set theory, sets are crisp, meaning that objects in the set are either in it or not in it. In our case, this implies that you’re certain that Uber’s business model should include a rating system or integrated payments. The fuzzy set idea throws a wrench in this equation. Each element in a fuzzy set has a membership function in the real interval [0,1], essentially making membership in the set more dynamic and contingent. Bringing this back to our example, it’s no longer guaranteed that trust is a big part of the problem or there will be a high volume of rides. Those are functionally contingent.

This seems relatively straightforward, but thinking about business models and problem spaces through the lens of fuzzy sets clarifies my own thinking because it attaches a function and dependency to every element considered.

So what?

Why is this helpful at all? The features or elements that constitute each of these sets (business model / problem) become subject to constant testing and validation. They become reactive to market conditions and sentiments.

Classifying things within models matters, and it gives us more ease in the uncertain world of startups. Additionally, for all these “fit” frameworks (product-market, founder-market, etc.), I think there’s a pseudo-predictive force at play. If we know what different types of “fit” look like in the past, maybe there’s a formulaic way to recreate parts of them in the future.

If you enjoyed this post, feel free to get in touch with me at aashaysanghvi[at]gmail.com.