The laws of classical logic assume that a proposition must have a certain value – truth or false (in other words, 0 or 1). This is often called the law of the excluded middle. In fact, the situation where we can assign specific condition to a particular category happens very rarely. It is hard, for example, to say exactly whether a person is high or short. You can’t set a fixed border at, let’s say, 180 cm. We are dealing here with linguistic values that can not be accurately represented by numerical values. The boundaries of these two sets (of high and short people) are not sharp.
Fuzzy logic gives a solution to this problem. Meaning of many notions depend upon their context and cannot be defined precisely. Their value lies in the middle, between “true” and “false”. Fuzzy logic can handle the concept of linguistic variables such as slow-fast, hot-cold, short-high. This makes it applicable in systems where there are more than two possible values. Automatic air conditioning or Anti – Lock Break System (ABS) are a good example of the use of fuzzy logic.
The fuzzy logic process can be divided into three stages. First of them is fuzzification. Here, traditional variables which represent exact quantities are assigned to fuzzy sets, which represent linguistic terms. Because these variables will most likely fit into more than one set, they are given certain degrees of membership. If we assign the following values to the sets describing the air temperature – 5-15 °C “low”, 10-20 °C “medium” – then the 12 °C value will belong to the “low” set with 0.4 degree, and to the “medium” set with 0.6 degree.
The second step is evaluation of the rules. The values obtained in a fuzzification process are confronted with the decision matrix based on a pre-defined IF-THEN rules. This allows to automate the decision making process. An example rule can be formulated as follows: IF the temperature is “low” and humidity is “medium” THEN set the speed of heating fan at “slow”.
The last step is defuzzification. As we remember the input data is assigned to the fuzzy sets with certain degree of membership. This also applies to the output. The process of defuzzification allows to obtain the crisp results by transforming the fuzzy information into certain value e.g. speed of heating fan.
Fuzzy logic provides a way to implement linguistic variables into computing. It gives the artificial systems a possibility to deal with nonlinear and imprecise problems. This makes fuzzy logic perfect for control systems in industry or public transport.
Nevertheless, it isn’t always an ideal solution. It requires manual tuning of membership functions and other parameters which might be tedious and time-consuming. In some cases conventional controllers are more efficient. Fuzzy logic doesn’t scale well to large and complicated problems.
Technologies based on fuzzy logic, however, are constantly evolving, and combining them with projects such as neural networks can provide a solution to create efficient, artificial decision-making systems.
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