Metric properties of the nearest extended parametric fuzzy number and applications

We propose the notion of extended parametric fuzzy number, which generalizes the extended trapezoidal fuzzy number and parametric fuzzy number, discussed in some recent papers. The metric properties of the nearest extended parametric fuzzy number of a fuzzy number, proved in the present article, help us to obtain the property of continuity for the parametric approximation operator and to simplify the solving of the problems of parametric approximations under conditions.