### Fuzzy Vector :-

Fuzzy vector is a vector containing fuzzy membership values. Suppose,

fuzzy set A defined on n elements in x1, x2, x3,………….,xn

fuzzy set B defined on m elements in y1, y2, y3,…………,ym

Then fuzzy networks vector is given by

Fuzzy vector can also be defined as a one dimensional array of membership values.

An array or a vector

is called a fuzzy vector, if for any element 0 ≤ a_{i} ≤ 1 ( ∀ i ∈ [1, n] )

### Transpose of a Fuzzy Vector

If A and B are two fuzzy vectors of length ‘n’ then

- The compliment of a fuzzy vector is given by
It is also a fuzzy vector since its values ∈ [0, 1]

- The largest element in the fuzzy vector ‘a’ is called its upper bound.
The smallest element in the fuzzy vector ‘a’ is called as its lower bound.

Here is an illustrative example for finding fuzzy inner product and fuzzy outer product:

Here, n is the min operator and V is the max operator.