In fuzzy-set theory, an element has a varying degree of membership, say dA, to a given set A instead of the traditional membership choice (is an element/is not an element).
In MMM[1] each index term has a fuzzy set associated with it. A document's weight with respect to an index term A is considered to be the degree of membership of the document in the fuzzy set associated with A. The degree of membership for union and intersection are defined as follows in Fuzzy set theory: