What are fuzzy sets? Describe the importance of fuzzy sets. Compare it with classical sets?
Answers
Classical Sets
the universe of discourse is the universe of all available information on a given problem
a universe of discourse , X, as a collection of objects all having the same characteristics
The clock speeds of computer CPUs
The operating currents of an electronic motor
The operating temperature of a heat pump (in degrees Celsius)
The Richter magnitudes of an earthquake
The integers 1 to 10
The individual elements in the universe X will be denoted as
x. The features of the elements in X can be discrete, countable integers or continuous valued quantities on the real line.
The total number of elements in a universe
X is called its cardinal number , denoted n x
Fu zzy Sets
Elements of a fuzzy set are mapped to a universe of
membership values
using a
function
-
theoretic form.
fuzzy sets are denoted by a set symbol with a tilde understrike;
A
∼
would be the
fuzzy set A.
This function maps elements of a fuzzy set
A
∼
to a real numbered value on the
interval 0 to 1.
If an element in the universe, say
x, is a member of fuzzy set
A
∼
, then this mapping
is given
by