# Fuzzy Neural Networks--A Review with Case Study
## 2 Fuzzy Neural Network Description
### Papers Summary  
The aims of using fuzzy neural networks are summarized in Table 1. As observed, fuzzy neural networks are primarily utilized for image recognition, data prediction, and control systems. Table 2 presents the correlations between the types of networks used and their respective aims. It is evident that the self-organizing networks are the more flexible solutions. However, these solutions require the definition of rules and membership functions.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**The Aim of Using Fuzzy Neural Network** & **Papers** \\ \hline Image recognition and clustering & [8; 9; 31; 32; 36; 52; 57; 65; 71] \\ \hline Data prediction in economy/business & [29; 34; 73] \\ \hline Data prediction & [24; 44; 48; 51; 53; 54; 58; 61; 63; 68; 74; 75] \\ \hline Control systems & [10; 12; 13; 15; 18; 23; 33; 35; 37; 38; 41; 49; 50; 56; 59; 60; 62; 64; 66; 67; 72] \\ \hline Navigation and positioning & [14] \\ Recommendation & [4; 11; 25; 30] \\ \hline Signals analysis & [17; 27; 42; 43; 55] \\ Data forecasting & [28] \\ \hline Trajectory control & [45; 46; 47; 69; 70] \\ \hline Reinforcement learning & [16] \\ \hline \hline \end{tabular}
\end{table}
Table 1: The aim of using fuzzy neural network.  
As can be noticed, the fuzzy network solutions are widely used for systems control, data prediction, and image recognition/clustering. The author is still working on their own solutions.  
FALCON and ANFIS networks are widely known. One fuzzy network solution is the application of Ordered Fuzzy Numbers to represent the weights of neurons.  
This review aims to compare fuzzy network solutions:  
* (a) Widely described in the literature in terms of potential usage;
* (b) With available code implemented in the network or its description.  
The comparison of fuzzy networks in this publication aims to:  
* (a) Demonstrate the feasibility of using these networks in terms of their simplicity compared to available neural network solutions in well-known frameworks;
* (b) Evaluate the results obtained by these networks using a well-known dataset in comparison to established solutions.  
The next chapter presents selected fuzzy networks.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithms/Network** & **Numbers of Papers** & **Aims** \\ \hline ANFIS & [27; 29; 30; 64] & \(\begin{array}{l}-Signals/data analysis\\ -control systems \\ \end{array}\) \\ \hline Type-2 network & [32; 36; 49; 50; 52; 54; 59; 60; 67] & \(\begin{array}{l}-Image recognition and clustering\\ -Control systems \\ \end{array}\) \\ \hline Ordered Fuzzy Numbers in & [74; 75] & \(\begin{array}{l}-Data prediction \\ -Data prediction \\ \end{array}\) \\ Deep Neural Network & [18] & \(\begin{array}{l}-Control systems \\ \end{array}\) \\ \hline Recurrent neural network & [17; 25; 45; 55; 66; 67; 72] & \(\begin{array}{l}-Recommendation\\ -Trajectory control \\ -Signals analysis \\ \end{array}\) \\ \hline Null uninorm & [4] & \(\begin{array}{l}-recommendation\\ \hline Takagi-Sugeno-Kang & [24] & \(\begin{array}{l}-data prediction \\ \end{array}\) \\ \hline BAM network & [35] & \(\begin{array}{l}-Control systems \\ \end{array}\) \\ \hline T-S fuzzy neural network & [58; 63] & \(\begin{array}{l}-Data prediction \\ \end{array}\) \\ \hline Min-max classifier & [65] & \(\begin{array}{l}-Image recognition and clustering \\ \end{array}\) \\ \hline Fuzzy graph neural network & [71] & \(\begin{array}{l}-Image recognition and clustering \\ -Control systems \\ -Data prediction in \\ economy/business \\ -Signals analysis \\ -Trajectory control \\ \end{array}\) \\ \hline \end{tabular}
\end{table}
Table 2: Type of fuzzy neural network used.