A fuzzy system is a kind of important tool to deal with uncertain informations through some fuzzy rules, Mamdani fuzzy system is one of the most simple high-dimensional system models. Firstly, this article points out that the traditional decomposition of Mamdani fuzzy system exists errors in theory, the actual dimension formulas of 2-dimensional and 3-dimensional Mamdani fuzzy systems are analyzed. And then, the lowering dimension decomposition formulas of $n$-dimensional systems based on the center indexs of the consequent fuzzy sets are obtained. Finally, an example is given to illustrate the decomposition formula not only can reduce the space's dimensions of a high-dimensional Mamdani fuzzy system, but also can reduce the total number of fuzzy rules within the fuzzy system.