The design and response abilities of time-varying fuzzy systems are discussed. Firstly, based on non-singleton fuzzifier and dynamic fuzzy inference method, the response function of time-varying fuzzy system is obtained. Then, a sufficient and necessary condition for time-varying fuzzy system possessing interpolation property is given. It is proved that time-varying fuzzy systems determined by t-norm or regular implication operators can be represented as some interpolation functions. Further, two sufficient conditions for time-varying fuzzy systems satisfying fitted properties are deduced. At last, a simulation result shows the effectiveness of the conclusion.