# Fuzzy Statistics: Simple Definition, Examples

Fuzzy statistics usually refers to a combination of fuzzy set theory—the treatment of ambiguous, imprecise, or subjective data—and traditional stats methods. It’s a very loose term that isn’t very well defined; Technically, it could apply to anything to do with fuzzy sets and statistics. Therefore, you’ll want to pay close attention to a particular author (or teacher’s) context when deciding what exactly they are referring to.

In a colloquial sense, it could simply mean statistics that aren’t clear. For example, this Washington Post article refers to the “fuzzy statistics” of pet ownership.

## Fuzzy Set Theory

In one definition of the term, fuzzy set theory forms the backbone of fuzzy statistics. In classical set theory, a member of a set either belongs to a set, or it doesn’t. This black and white approach, similar to binomial experiments, makes for clear lines between data types. It also makes it easier to draw conclusions about data.

On the other hand, fuzzy set theory blurs the lines of set membership, assigning elements to a set based on membership functions.

## Methods of Fuzzy Statistics

Fuzzy statistics includes a wide range of methods and theories, including:

• Fuzzy Bayesian statistics,
• Fuzzy estimation,
• Fuzzy hypothesis testing,
• Fuzzy regression.

In simple terms, the moniker “fuzzy” means to take one of the established theories and blur the lines a little. You could view this as stretching the boundaries, or even breaking the rules. As you can probably imagine, not everyone breaks the same rules so this means that the methods involved with fuzzy statistics are not very well defined. For example, some authors (e.g. Buckley) recommend starting with crisp (non-fuzzy) data to generate estimators. Other authors start with fuzzy data and attempt to create meaningful estimators.

## References

Buckley, J. (2013). Fuzzy Statistics. Springer.
Taheri, M. (2016). Trends in Fuzzy Statistics. Retrieved February 13, 2020 from: https://www.semanticscholar.org/paper/Trends-in-Fuzzy-Statistics-Taheri/1aeabf696923eab6724a3a3140d30018050df79e
Zadeh, L. (Ed.) et al. (1975). Fuzzy Sets and their Applications to Cognitive and Decision Processes. Proceedings of the US–Japan Seminar on Fuzzy Sets and their Applications, Held at the University of California, Berkeley, California, July 1–4.

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Stephanie Glen. "Fuzzy Statistics: Simple Definition, Examples" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/fuzzy-statistics/