New operational laws and aggregation method of intuitionistic fuzzy information

Atanassov [Intuitionistic fuzzy set, Fuzzy Sets and Systems 20 (1986), 87-96] introduced intuitionistic fuzzy set (A-IFS), whose basic elements are intuitionistic fuzzy numbers (IFNs). The IFN is an ordered pair, which is described by a membership degree, a non-membership degree and a hesitancy degree. The weights of all the existing exponential operational laws and the corresponding aggregation methods for IFNs are non-negative real numbers in unit interval. As a supplement, a new exponential operational law about IFNs is defined, in which the bases are positive real numbers and the exponents are IFNs. Then some properties of the operational law are investigated, and an intuitionistic fuzzy information aggregation method is given. Finally, a practical example is illustrated to show the applicability of the operational law and the aggregation method.