Fuzzy logic - definition

Fuzzy logic (fuzzy logic) is a generalisation of classical bivariate logic, in which the logical values are not restricted to the state of truth (1) or falsity (0), but can take any intermediate value from the interval [0, 1]. This concept allows the mathematical modelling of imprecise, ambiguous or partially true information, which finds application in the description of phenomena that are difficult to classify unambiguously.

The basis of fuzzy logic is fuzzy sets, whose membership is not described by an unambiguous criterion, but by a membership function that determines the degree to which a given element belongs to a given set. This makes it possible to formally represent natural language concepts such as 'warm', 'fast' or 'big', which have no sharp boundaries.

Systems using fuzzy logic operate on if-then rules, in which premises and conclusions can be imprecise. The inference process based on fuzzy rules allows decisions to be made on the basis of incomplete or uncertain data, with continuity and stability of operation. The final result, represented as a fuzzy value, can then be defuzzified to produce a specific control value.

Fuzzy logic has found widespread use in control engineering, Automation, robotics and expert systems, especially where traditional mathematical models prove too complex or inadequate. It enables the design of adaptive and flexible algorithms that better represent human behaviour and the characteristics of non-linear physical systems. Its popularity is due to its ability to be implemented in real time and its good tolerance to errors and noise in the input data.

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