Definition:Fuzzy Set

Definition

Let $S$ be a set.

Let $\closedint 0 1$ denote the closed unit interval.

Let $\mu: S \to \closedint 0 1$ be a mapping.

Then $\struct {S, \mu}$ is a fuzzy set.

Domain

$S$ is the domain of $\struct {S, \mu}$.

Membership Function

$\mu$ is the membership function of $\struct {S, \mu}$.

Also see

• Results about fuzzy sets can be found here.

Sources

• 2000: Kenneth H. Rosen and John G. Michaels: Handbook of Discrete and Combinatorial Mathematics: $\S 1.7.2$