Prerequisite: Fuzzy Logic | Introduction

**Fuzzy Inference System (FIS)** is a process to interpret the values of the input vector and, on the basis of some sets of fuzzy rules, it assigns corresponding values to the output vector. This is a method to map an input to an output using fuzzy logic. Based on this mapping process, the system takes decisions and distinguishes patterns.

There are two main types of fuzzy inference systems: **Mamdani FIS** and **Sugeno FIS**.

## Mamdani FIS –

The Mamdani fuzzy inference system was proposed by Ebhasim Mamdani. Firstly it was designed to control a steam engine and boiler combination by a set of linguistic control rules obtained from the experienced human operators. In Mamdani inference system, the output of each rule to be a fuzzy logic set.

## Sugeno FIS –

This fuzzy inference system was proposed by Takagi, Sugeno, and Kang to develop a systematic approach for generating fuzzy rules from a given input-output dataset. A typical fuzzy rule in a first-order Sugeno fuzzy model has the form:**IF x is A and y is B THEN z = f(x, y)**

where

- A and B are fuzzy sets in the antecedent
- z = f(x, y) is a crisp function in the consequent.

Higher-order Sugeno fuzzy models are also possible, but while designing, those introduce significant complexity.

**Difference Between Mamdani and Sugeno Fuzzy Inference System:**

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 |

Though there is one similarity worth be mentioned between Mamdani and Sugeno Fuzzy Inference System, the antecedent parts of these both of the FIS rules are same.