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# Comparison Between Mamdani and Sugeno Fuzzy Inference System

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 FISSugeno FIS
Output membership function is presentNo output membership function is present
The output of surface is discontinuousThe output of surface is continuous
Distribution of outputNon distribution of output, only Mathematical combination of the output and the rules strength
Through defuzzification of rules consequent of crisp result is obtainedNo defuzzification here. Using weighted average of the rules of consequent crisp result is obtained
Expressive power and interpretable rule consequentHere is loss of interpretability
Mamdani FIS possess less flexibility in the system designSugeno FIS possess more flexibility in the system design
It has more accuracy in security evaluation block cipher algorithmIt 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) systemsIt is using only in MISO (Multiple Input and Single Output) systems
Mamdani inference system is well suited to human inputSugeno inference system is well suited to mathematically analysis
Application: Medical Diagnosis SystemApplication: 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.