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We devote to study the arithmetic operator of fuzzy regular prismoid numbers as well as the degree of similarity between fuzzy regular prismoid numbers, and then the arithmetic operator and the degree of similarity are applied in risk analysis. Firstly, the arithmetic operator of fuzzy regular prismoid numbers are researched, and some properties of the arithmetic operators are discussed. At the same time, the fuzzy regular prismoid numbers approximation of 2-dimensional fuzzy numbers is discussed as an indispensable part to study the fuzzy risk analysis. Then, the degree of similarity between fuzzy regular prismoid numbers are deeply researched, which are the basic work of studying the fuzzy risk analysis. Finally, the proposed results are applied in risk analysis of a company.

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.

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]

We use the concept of generalized difference for fuzzy n-cell numbers which is presented in this paper to introduce and study the differential and gradient of fuzzy n-cell mappings. At the same time, some connections between gradient, boundary-function-wise gradient and level-wise gradient of fuzzy n-cell mappings are established. Furthermore, the subdifferential for fuzzy n-cell mappings based on the ordering ...c is discussed. [ABSTRACT FROM AUTHOR]