Search

In this paper, the concepts of differentiability and gradient for fuzzy mappings are presented and discussed using the characteristic theorem for generalized difference of n dimensional fuzzy numbers. The relationships of gradient, support-function-wise gradient and level-wise gradient are characterized. [ABSTRACT FROM AUTHOR]

Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods. [ABSTRACT FROM AUTHOR]