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精确描述借助于一定的测量仪器，用确定的量来表示物质的属性。精确数学在思想方法和推理形式上属于“非此即彼”的二值逻辑。精确控制以精确数学的精确表达为前提，在一定条件下是必要的，也是有效的，但对大量的不能用精确数学描述的过程却无能为力。模糊描述则是用非确定的量来表示物质的属性，侧重于描述事物相互对比的属性。模湖数学是研究和处理模糊现象的科学，在思维方法和推理形式上属于“亦此亦彼”多元逻辑。以模糊数学为基础的模糊控制在本质上是一种智能控制。
Accurate description by means of a certain measuring instrument, with a certain amount of material properties. Precise mathematics belongs to the binary logic of “not one or the other” in the way of thinking and reasoning. Precise control, premised on accurate mathematical expression, is necessary and effective under certain conditions, but it can not do it for a large number of processes that can not be described by precise mathematical methods. Fuzzy description uses nondeterministic quantities to represent the attributes of matter, and focuses on the attributes that describe the contrast between things. Mathematical modeling mathematics is to study and deal with the phenomenon of fuzzy science, in the way of thinking and reasoning forms belong to “also so” pluralistic logic. Fuzzy control based on fuzzy mathematics is essentially an intelligent control.