Fuzzy functions (Q1311891)

The author defines a fuzzy function \(\mathbb{R}\) from \(X\) to \(Y\) as a special fuzzy relation on \((X,Y)\), i.e. a special fuzzy set on \(X\times Y\). A concept of ``nearly equal'' (called fuzzy equality) is introduced with the aid of a metric. Thus if two points are ``nearly equal'', then the points transferred by a fuzzy function are also ``nearly equal''. A formula for calculating the grade of ``nearly equal'' is suggested as well.