Fuzzy Logic

Fuzzy sets are combined using standard operators [21,18]. The inverse, $\bar{A}$, of a set, $A$, has the membership function $f_{\bar{A}}(a) = 1-f_A(a)$ where $f_A(a)$ is the membership of element $a$ in the set A. In the rest of this paper, we will represent $f_A(a)$ by $f_A$ when we talk about a relationship valid over all the elements in the universe of discourse. The membership of an element in the union of two sets ($A \cup B$) is given by the maximum of memberships in the two sets ($f_A \vee f_B$). This represents a logical OR. The membership of an element in the intersection of two sets ($A \cap B$) is given by the minimum of the two sets' memberships ( $f_A \wedge f_B$) and represents a logical AND.