In this post I will give an introduction do fuzzy logic. It is an important element in artificial intelligence, process control and computational systems. Information in natural language are converted in binary values.

**Concepts**

The Boolean logic is binary and deal with zeros or ones, true or false, etc. While the fuzzy logic deal with intermediary values between the absolute values. In this logic, 0 and 1 or false and true are used as minimum and maximum limits respectively. The left graphic shows Boolean logic and the right graphic shows fuzzy logic.

The areas in the fuzzy logic graphic are called membership function. Here is a exemple of fuzzy logic graphic to determinate a person`s age.

This type of logic also uses the concept of fuzzy set without well defined border, can say that a valor can have 60% from a set and 40% from other. In this case it has membership degree of 0,6 in a set and 0,4 in another. In opposition to Boolean logic which says that it must belong to a set or not. The sets have a name which is linguistic variable.

**Fuzzy system**

Below we have a block diagram of fuzzy logic system.

The inference is made in the logic decision unit using data and rules from the base. The fuzzificator transform binary input data in language values, the data are framed in sets and is determined the membership degree to the sets. The defuzzificator convert fuzzy values in binary values. There are three defuzzification methods:

- Max membership method: Choose data with maximum value;
- Centroid method: Determine the central point in the membership function calculating the output`s weighted mean;
- Weighted average method: Assign weight to each membership function in the output.

**Applications**

Some applications of fuzzy logic:

- Camera with automatic zoom;
- System modeling, decision taking and standard reconnaissance to robots;
- Computation with words in specialist systems;
- Control systems with sensors to control actuators reducing power consumption, for example, an air conditioner with temperature sensor controlling the power;
- ABS breaker.