Fuzzy Inference System(FIS): A Detailed Guide For 2021


The fuzzy inference system is an important part of the fuzzy logic system. The main work that it performs is decision-making. It makes use of the rules of IF and THEN along with the AND and OR connectors which in turn lets it draw some essential rules for decision making.

In this article let us look at:

  1. Characteristics of Fuzzy Inference System
  2. Functional Blocks of FIS
  3. Working of FIS
  4. Methods of FIS

1. Characteristics of Fuzzy Inference System

Here are the characteristics of the fuzzy inference system.

  • The output that is received from the fuzzy inference system will always be a fuzzy set. This is irrelevant to what the input is. The input can either be crisp or fuzzy.
  • If fuzzy is used in the form of a controller, then it must always throw a fuzzy output.
  • There is a defuzzification unit always present with the fuzzy inference system. It helps to covert the variables that are fuzzy into crisp variables.

2. Functional Blocks of FIS

Fuzzy has in total five functional blocks that will let you understand its construction in detail.

  • The rule base consists of the IF-THEN rules of fuzzy.
  • The database defines the fuzzy sets of membership functions that are applied in the fuzzy rules.
  • The decision-making unit carries out operations on the fuzzy rules.
  • The fuzzification interface unit helps to convert any crisp quantity into a fuzzy quantity.
  • The defuzzification interface unit will convert any fuzzy quantity into a crisp quantity.

3. Working of FIS

The complete working of the fuzzy inference system can be divided into these steps.

  • The fuzzification unit will support the numerous applications of the fuzzification methods. It will then convert the input that is crisp into a fuzzy input.
  • There will be a knowledge base collection of the rule-based database, which gets formed when the crisp input is converted to a fuzzy input.
  • Finally, the defuzzification unit fuzzy input will be converted into a crisp output.

4. Methods of FIS

There are two different types of fuzzy inference system which have a different consequent of the fuzzy rule. These are the Mamdani fuzzy inference system and the Takagi-Sugeno Fuzzy Model or the TS Method.

Mamdani Fuzzy Inference System

The system was originally proposed by Ebhasim Mamdani in the year 1975. The Mamdani fuzzy inference system was anticipated to control a combination of a boiler and a steam engine which was done by synthesizing a group of fuzzy rules that was obtained by those who were employed on the system.

Steps to compute the output

The following steps are followed to compute the fuzzy inference system output:

  • In the first step, a set of fuzzy rules has to be determined.
  • In the next step, the input membership function is used to make the input fuzzy.
  • The strength rule is established, which is done by combining the fuzzy inputs as per the rules of fuzzy.
  • The rules consequent is determined, which is done by combining the strength of the rule and the function of output membership.
  • All the consequent are not combined to get the output distribution.
  • Finlay, you get a defuzzified output distribution.

Takagi-Sugeno Fuzzy Model (TS Method)      

The TS model was proposed by Sugeno, Kang, and Takagi in the year 1985. Here is the rules format.

IF x is A and y is B THEN Z = f(x,y)

In this case, AB is the fuzzy set in the antecedents, and z = f(x,y) in the consequent is a crisp function.

The fuzzy inference process under the TS method

Here is how the fuzzy inference process works under the TS method

  • The input is fuzzified in the first step. In this case, the input of the system is made fuzzy.
  • Then the fuzzy operator is applied, which is important to get the output.

Comparison of the two methods

Here is a comparison of the Mamdani and Sugeno fuzzy inference systems

  • The main difference between the two lies in the output membership function. The membership function in the case of the Sugeno Model is constant or linear.
  • The fuzzy rule consequences cause a difference in the defuzzification and the aggregation procedures.
  • The Sugeno rules are more mathematical in comparison to the Mamdani rule.
  • There are more adjustable parameters in the Sugeno controller in comparison to the Mamdani controller.


FIS is a framework that uses fuzzy logic and depicts the process of connecting any input into its output. The main building blocks of the fuzzy inference system are fuzzification, membership function, and defuzzification.

The fuzzy IF and THEN rule is employed to express the relationship between input and output, which helps to model the qualitative input, which in turn helps to create an output. There are a set of consequent and antecedent fuzzy inference system and some IF-THEN rules of fuzzy, which is a firm basis of the core of a system. This, in turn, is used to make decisions in conditions that are inaccurate or vague.

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