# What is Fuzzy Inference System and How it works?

What is Fuzzy Inference System (FIS)? A fuzzy inference system is a key component of any fuzzy logic system. It uses fuzzy set theory, IF-THEN rules and fuzzy reasoning process to find the output corresponding to crisp inputs. Predicates in IF-THEN rules are connected using *and *or *or* logical connectives.

## Characteristics of FIS:

- Read crisp value from the process
- Maps the crisp value into fuzzy value using the fuzzy membership function
- Apply IF-THEN rules from the fuzzy rule base and compute fuzzy output
- Convert fuzzy output into crisp by applying some defuzzification methods.

## How fuzzy inference system works?

Crisp input of any process (measuring temperature of air conditioner, measuring altitude, attitude, height, angle of direction for aeroplane etc. ) is given to the fuzzifier, which applies fuzzy membership function and maps the actual readings into fuzzy value (i.e. the value between 0 to 1).

The inference engine applies fuzzy rules from the knowledge base and produces the fuzzy output, which is again between 0 and 1. This output can not be used directly in any process or system. It needs to be mapped into the original domain. Defuzzifier is the inverse process of fuzzification, it converts the fuzzy output into crisp output, which can be fed to the process. Crisp sets are internally converted to fuzzy sets.

Let’s take the scenario of the air conditioner. For simplicity, we will consider only one parameter which determines the temperature of the air conditioner to be set. Let us consider that the temperature of an air conditioner depends on the parameter called room temperature.

Let us divide the range of room temperature into cool, nominal and warm. Any temperature value may belong to multiple sets with different membership values. The value t = 20 has a membership value of 1 in the nominal set and 0 in the other two. If we move to the right, the membership value in the nominal set decreases and in the warm set, it increases. And as we move left from t = 20, the membership value in the nominal set decreases and in the cool set it increases

Any room temperature is converted to fuzzy value using such fuzzification methods (here we have used triangular membership function, more are discussed later in this article). And that input goes to the inference engine, which will determine what should be the temperature of the air conditioner. Assume that the internal representation of that temperature belongs to the increase and decrease set.

So the generated output might have some membership for both the increase and decrease sets. Assume that it’s 0.7 for increased class and 0.15 for decreased class. Although output is computed, it can not be given directly to the controller of AC, because the controller does not understand what is meaning of the membership value of temperature 0.7 in the increase class and 0.15 in the decrease class.

A number of defuzzification methods are there which can be used to convert this fuzzy output into a crisp one. For a particular instance, the crisp output may be -4, which says reducing the temperature of the air conditioner by 4 degrees.

## Approaches for Fuzzy Inference System

The following are the popular approaches to fuzzy inference systems. The antecedent part of all rules remains the same, they differ only in the consequent part.

- Mamdani fuzzy inference system
- Takagi-Sugeno fuzzy inference system
- Tsukamoto fuzzy inference system

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## Test Your Knowledge !

- Which is the first step in FIS? Applying fuzzy rules, defuzzification or fuzzification?
- Why fuzzification is necessary?
- Why do we need defuzzification?