Abstract: In order to apply the fuzzy system based on the QIP algorithm well in practice, research on responsiveness and general approximation of such fuzzy systems is of great significance. In this paper, the fuzzy inference expression of 5-I algorithm based on S implication and Zadeh implication is proposed. Furthermore, by using single-point fuzzification and gravity center defuzzification method, we find that for S implication and R implication, a single-input single-output (SISO) fuzzy system based on QIP algorithm has only step output conditions and can not approximates a function well. The preceding property does not necessarily exist in such fuzzy systems with Zadeh implication. In addition, in the multi-rule SISO fuzzy system based on QIP algorithm, fuzzy reasoning is independent of the order of aggregation under certain conditions. Finally, a concrete example is provided to demonstrate responsiveness and universal approximation of fuzzy systems based on the five-I algorithm.

Key words: fuzzy reasoning, fuzzy system, quintuple I algorithm, implication operator, response function