# Modeling of Fuzzy Systems Based on the Competitive Neural Network
## 1 Introduction  
Computer sciences have developed rapidly and researchers around the world in the field on artificial intelligence [1] have applied multiple algorithms for optimization, clustering, and classification problems. One of the challenges is to extract meaningful patterns in large datasets. This is where clustering and classification, two basic concepts in machine learning, play a transformative role. As datasets grow in size and complexity, the demands on algorithms to adapt and scale also increase.  
The most famous optimization algorithms are based on swarm optimization, such as Particle Swarm Optimization (PSO) [2], Fireworks Algorithm (FWA) [3], Gravitational Search Algorithm (GSA) [4], and Grey Wolf Optimizer (GWO) [5], etc. In the field of clustering, we can find the Fuzzy C-Means [6] and K-Means clustering [7] algorithms. For classification tasks, we can explore algorithms such as K-Nearest Neighbors [8] or robust artificial neural networks [9].  
Artificial neural networks can be divided into two classes depending on the type of learning they use: neural networks with supervised learning and neural networks with unsupervised learning [10]. It is important to highlight this aspect because the challenge that we are going to attack in the proposed method involves the utilization of an artificial neural network with unsupervised learning, specifically, with a Competitive Neural Network (CNN), which is a technique in the area of clustering [11, 12] and not in the classification area.  
On the other hand, according to the state of the art method, a plethora of researchers have used Fuzzy Inference Systems, FISs, to solve different types of problems, for example, by dynamically adjusting parameters [13] in optimization algorithms, in controlproblems [14], as well as prediction [15] and classification tasks. These latter problems have been solved with better accuracy, especially when working with noisy datasets, thanks to the ability of fuzzy inference systems to model the uncertainty present in the information [16; 17].  
All methods have strengths and weaknesses; therefore, part of the main the contribution of this paper is to generate an intelligent hybrid method using the potential of the CNN to cluster and aggregate the classification task by implementing Fuzzy Inference Systems. In the approach, first the CNN is performed to obtain the clusters and centroids of the input data, after that the Type-1 FIS is automatically designed according to the output produced by the CNN. Thus, another contribution of this paper is the methodology to dynamically generate the parameters of the input and output membership functions MFs of the FIS and these can be adapted according to the dataset classification problem used. In the approach, two FIS models were considered using Sugeno and Mamdani. Furthermore, these models are generated using three types of MFs (Trapezoidal, Gaussian, and Triangular) to have more variants in the models and analyze the behavior and precision obtained. The general approach is applied to three datasets (Wine, Iris, and WDBC) to measure the performance and accuracy of these algorithms in classification tasks.  
This paper is organized as follows. Section 2 explains the theoretical concepts, techniques, and components that were used to develop this work. Section 3 presents the general proposal, describing the methodology to dynamically generate the Mamdani Type-1 FIS and Sugeno Type-1 FIS with different types of MFs. Section 4 explains the experimental results obtained with the proposed methods after being applied to the three databases. Finally, Section 5 offers the conclusions based on the results and some future works.