The concept of a linguistic variable and its application to approximate reasoning - II

DEFINITION 1.1. A fuzzy variable is characterized by a triple (X, U, R (X;u)). in which X is the name of the variable; U is a universe of discourse (finite or infinite set); u is a generic name for the elements of U; and R(X;u) is a fuzzy subset of U which represents a fuzzy restriction on the values of u imposed by X. [As in the case of nonfuzzy variables, R(X;u) will usually be abbreviated to R(X) or R(u) or R(x), where x denotes a generic name for the values of X, and R(X;u) will be referred to as the restriction on u or the restriction imposed by X.1 The nonrestricted nonfuzzy variable u constitutes the base variable for X. The assignment equation for X has the form