Definition:Fuzzy Intersection

Definition

Let $\mathbf A = \struct {A, \mu_A}$ and $\mathbf B = \struct {B, \mu_B}$ be fuzzy sets.

Then the (fuzzy) intersection of $\mathbf A$ and $\mathbf B$ is denoted $\mathbf A \cap \mathbf B$, defined as the fuzzy set such that:

The domain of $\mathbf A \cap \mathbf B$ is $A \cap B$

The membership function of $\mathbf A \cap \mathbf B$ is:

$\forall x \in A \cap B: \map {\mu_{A \cap B} } x = \map \min {\map {\mu_A} x, \map {\mu_B} x}$

where $\min$ is the min operation.

Sources

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