Fuzzy Neural Networks (FNNs) is a type of Artificial Neural Network (ANN) that combines the principles of fuzzy logic and neural networks to model complex, non-linear systems. They are designed to handle uncertainty, imprecision, and vague data, which are often encountered in real-world applications.

Fuzzy logic is a mathematical framework that deals with uncertainty and imprecision in a more flexible and intuitive manner than traditional Boolean logic. It provides a set of tools for modeling and control systems that are not fully understood or that are subject to uncertainty and imprecision. Fuzzy logic has been applied in a variety of fields, including control systems, decision-making, and data analysis.

Neural networks, on the other hand, are computer algorithms that are designed to mimic the structure and function of the human brain. They are capable of learning from data and making predictions based on patterns in the data. Neural networks have been applied to a wide range of applications, including image recognition, speech recognition, and natural language processing.

Fuzzy Neural Networks bring together the strengths of fuzzy logic and neural networks to provide a powerful tool for modeling complex systems. In a Fuzzy Neural Network, the input and output variables are described using fuzzy sets, which allow for the representation of imprecise or vague data. The network is then trained using a set of input-output pairs to learn the mapping between the inputs and outputs.

One of the key advantages of Fuzzy Neural Networks is their ability to handle uncertainty and imprecision in the data. They are able to make decisions based on partial or vague information, which is often encountered in real-world applications. Additionally, they are capable of making probabilistic predictions, which can be useful in situations where the outcomes are uncertain.

Fuzzy Neural Networks have been applied to a wide range of applications, including control systems, pattern recognition, and decision-making. They have been used in areas such as medical diagnosis, financial forecasting, and control systems for autonomous vehicles.