The extension principle is a basic concept in the fuzzy set theory that extends crisp domains of mathematical expressions to fuzzy domains. Suppose f(.) is a function from X to Y and A is a fuzzy set on X defined as:

A=ma(x1)/x1 + ma(x2)/x2 + ...... + ma(xn)/xn

Where ma is the Membership Function of A. the + sign is a fuzzy OR (Max) and the / sign is a notation (indicated the variable xi in discourse domain X - NOT DIVISION)

Then the extension principle states that the image of fuzzy set A under the mapping f(.) can be expressed as a fuzzy set B,

B=f(A)=ma(x1)/y1 + ma(x2)/y2 + ...... + ma(xn)/yn

where yi = f(xi) , i = 1,2,3,....,n