A discussion of algorithms for the max–min problem

The max–min algorithm in fuzzy mathematics is discussed. Liu considers that the widely-used max–min algorithm is incorrect. The paper shows that the Liu's conclusion is not true. Firstly, the max–min algorithm satisfies the needs of an operator for fuzzy synthetic evaluation. Secondly, the widely-used examples show the appropriate uses of the max–min algorithms. Finally, the max–min algorithm is based on other algorithms which may be used in fuzzy synthetic evaluation. So as a fuzzy synthetic evaluation method, the max–min algorithm not only has a mathematical basis but also has a practical use. But in some cases the max–min algorithm will be ineffective, so it also has shortcomings and needs to be improved. The improved max–min algorithm is given.