What is Fuzzy Inference System (FIS)? Fuzzy inference system is 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 fuzzy membership function
- Apply IF-THEN rules from 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 airplane 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).

Inference engine applies fuzzy rules from knowledge base and produce the fuzzy output, which is again between 0 and 1. This output can not be used directly into any process or system. It needs to be mapped into 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.

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

Let us divide the range of room temperature to cool, nominal and warm. Any temperature value may belong to multiple sets with different membership value. The value t = 20 has membership value 1 in nominal set and 0 in other two. If we move on right, the membership value in nominal set decreases and in warm set it increases. And as we move left from t = 20, the membership value in nominal set decreases and in 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 inference engine, which will determine what should be the temperature for air conditioner. Assume that the internal representation of that temperature belongs to increase and decrease set.

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

Number of defuzzifiction methods are there which can be used to convert this fuzzy output into crisp one. For particular instance, the crisp output may be -4, which says reduce the temperature on air conditioner by 4 degree.

## Approaches for Fuzzy Inference System

Following are the popular approaches to fuzzy inference system. Antecedent part of all rules remain same, they differ only in 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?