The arithmetic correlation function is a new method for studying the cryptographic properties of Boolean functions. Based on the basic definitions of addition and multiplication of multi-2-adic integer, the study constructed a new algebraic ring and realized the arithmetic or “with-carry” analogs of classic correlation functions. In this paper the definition of arithmetic autocorrelation function was introduced. The arithmetic correlation value of symmetric Boolean functions was studied. The results show that the arithmetic autocorrelation function of symmetric Boolean functions is a real symmetric function with at most n1 values.

In order to improve the accuracy of data decision making, an optimization approach was proposed for the algorithm of multi-objectives group decision making. By the interval-valued intuitionistic fuzzy set theory, the optimization was approached by the method of iterative computation gradually in the situation that the part weight information was incomplete usually. Results of the simulation indicate that the algorithm has low time complexity, and can be implemented in the computer easily; moreover, it also shows the effectiveness and accuracy of the algorithm.