# Definition:Fuzzy Set

## Definition

Let $S$ be a set.

Let $\left [{0 \,.\,.\, 1}\right]$ denotes the closed unit interval.

Let $\mu: S \to \left [{0 \,.\,.\, 1}\right]$ be a mapping.

Then $\left({S, \mu}\right)$ is a fuzzy set.

### Domain

$S$ is the domain of $\left({S, \mu}\right)$.

### Membership Function

$\mu$ is the membership function of $\left({S, \mu}\right)$.