先决条件：模糊逻辑|介绍
模糊推理系统(FIS)是一种解释输入向量的值的过程，并且基于一些模糊规则集，它将对应的值分配给输出向量。这是一种使用模糊逻辑将输入映射到输出的方法。基于此映射过程，系统将做出决策并区分模式。
模糊推理系统主要有两种类型： Mamdani FIS和Sugeno FIS 。
Mamdani FIS –
Mamdani模糊推理系统是由Ebhasim Mamdani提出的。首先，它被设计为通过从经验丰富的运算符那里获得的一套语言控制规则来控制蒸汽机和锅炉的组合。在Mamdani推理系统中，每个规则的输出都是模糊逻辑集。
Sugeno FIS –
Takagi，Sugeno和Kang提出了这种模糊推理系统，目的是开发一种从给定的输入输出数据集生成模糊规则的系统方法。一阶Sugeno模糊模型中的典型模糊规则具有以下形式：
如果x是A且y是B则z = f(x，y)
在哪里
- A和B是先验中的模糊集
- 因此，z = f(x，y)是一个明晰的函数。
也可以使用高阶Sugeno模糊模型，但是在设计时，这些模型会带来很大的复杂性。
Mamdani和Sugeno模糊推理系统之间的区别：
| Mamdani FIS | Sugeno FIS |
|---|---|
| Output membership function is present | No output membership function is present |
| The output of surface is discontinuous | The output of surface is continuous |
| Distribution of output | Non distribution of output, only Mathematical combination of the output and the rules strength |
| Through defuzzification of rules consequent of crisp result is obtained | No defuzzification here. Using weighted average of the rules of consequent crisp result is obtained |
| Expressive power and interpretable rule consequent | Here is loss of interpretability |
| Mamdani FIS possess less flexibility in the system design | Sugeno FIS possess more flexibility in the system design |
| It has more accuracy in security evaluation block cipher algorithm | It has less accuracy in security evaluation block cipher algorithm |
| It is using in MISO (Multiple Input and Single Output) and MIMO (Multiple Input and Multiple Output) systems | It is using only in MISO (Multiple Input and Single Output) systems |
| Mamdani inference system is well suited to human input | Sugeno inference system is well suited to mathematically analysis |
| Application: Medical Diagnosis System | Application: To keep track of the change in aircraft performance with altitude |
尽管在Mamdani和Sugeno模糊推理系统之间有一个相似之处值得一提，但是这两个FIS规则的前一部分都是相同的。