What is a Fuzzy Vector

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 Network Vector equations

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

array-or-vector

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

Transpose of a Fuzzy Vector

transpose-of-a-fuzzy-vector

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

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

    find-fuzzy-inner-product-and-fuzzy-outer-product-example

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

  • The compliment of a fuzzy vector is given by
    compliment-of-a-fuzzy-vector

    It is also a fuzzy vector since its values ∈ [0, 1]

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

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

    lower-bound-of-fuzzy-vector

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