**1. Introduction**

Intelligent machine-learning-based models have assumed a prominent role in solving complex problems common in modern society. Intelligent methods can dynamically solve problems and optimize industry processes, disease diagnoses, or actions related to Internet transactions [1].

With the advent of the Internet in people's lives, and the popularization of e-commerce, a current problem is online shopping fraud. Some websites promote user interaction based on bids placed on a product or service. This online auction encourages users to buy products through bids that can be made remotely, according to the standards set by the platforms that offer this service. However, purchases involving high-value goods or rare items often suffer from fraud attempts. In general, online auction fraud has specific characteristics, ranging from products of dubious origin, suspicious and repetitive bidding on a particular item, overvaluation of a product through constant bidding, and users registering on the platform to cause trouble [2]. These problems can make the experience of buying a product at an online auction appalling, preventing new users from opting for this form of purchase and discrediting the platform that offers such services [3]. Considering the actuality of the

**Citation:** de Campos Souza, P.V.; Lughofer, E.; Rodrigues Batista, H.; Junio Guimaraes, A. An Evolving Fuzzy Neural Network Based on Or-Type Logic Neurons for Identifying and Extracting Knowledge in Auction Fraud. *Mathematics* **2022**, *10*, 3872. https:// doi.org/10.3390/math10203872

Academic Editors: Antonin Dvorak and Vilém Novák

Received: 20 September 2022 Accepted: 14 October 2022 Published: 18 October 2022

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problem, some researchers have built a database of factors that exist in auctions to identify fraud during transactions to prevent such problems from occurring [4]. These studies support significant areas of current research, and researchers worldwide are working to identify corresponding patterns and propose solutions, including approaches that use clustering and machine learning [5].

Machine-learning-based models can act to assist in the detection of fraud in online auctions. In particular, a model that can combine the efficiency of training artificial neural networks and interpreting fuzzy systems can solve this problem and extract knowledge of auction fraud through linguistic rules about the problem [6]. Fuzzy neural networks can process input data in fuzzy sets and, using neural network training, provide answers to problems with a high degree of interpretability, because this model is comprised of a fuzzy inference system that can represent data in a linguistic and interpretable way using fuzzy operations [7].

When accompanied by logical interpretability about the functioning of the models that act in this solution, this problem solving can facilitate humans' understanding and acceptance of results. Fuzzy natural logic (FNL) is a formal theory that aims to provide a mathematical model of natural human reasoning whose typical feature is using natural language. Its central basis is based on the results of linguistics, artificial intelligence, and logical analysis of natural language [8].

This paper proposes a new evolving fuzzy neural network architecture based on an empirical data analysis fuzzification process that applies the concepts of self-organized direction-aware data partitioning [9]. Logic neurons based on t-conorm (or-neurons) are in the model's second layer. The model's training is founded on Extreme Learning Machine [10] in the offline phase, and the evolving phase is established on indicator-based Recursive Weighted Least Squares [11]. The three-layer model has a fuzzy inference system connected to a neural aggregation network represented in its third (and last) layers. This combination of factors allows the third layer of the model to provide the network's output (defuzzification process) with answers about frauds in online auctions and fuzzy rules that express the logical and interpretable relations present in the evaluated dataset. The model also includes sophisticated capabilities for the behavior's interpretability throughout its analyses, demonstrating tendencies important to interpretability and information extraction. In addition, this paper proposes a presentation of knowledge about a dataset of fraud in auctions with IF–THEN rules, presenting the logical relationships between the dimensions of the problems and the possible impacts of discovering fraudulent behavior. The behavior of the weights of each dimension linked to the fuzzy sets generated gives an interpretative dimension to the issues present in identifying fraud.

The motivation for applying evolving fuzzy neural networks in dynamic behavior problem areas (such as auction fraud) is connected to the dynamic ability of these types of approaches to identify new behaviors from data, incorporating new neural structures into their architecture. Auction fraud problems have an extremely dynamic behavior, as the types of fraud are constantly changing (either by creating new techniques or when previous frauds are discovered). This evolution of knowledge on the models' components helps solve complex problems that can dynamically change over time. Stream data assessments require models to obtain assertive and adaptive outputs. Thus, evolving fuzzy neural networks act this way, with the advantage of demonstrating the evolution of knowledge and identifying behaviors of the elements of their fuzzy rules (antecedents and consequents).

This paper's main highlight is connected with an assertive and interpretable approach to the problem of fraud in auctions. Relations on validating interpretability criteria and generating fuzzy rules are presented to the reader. Another evolving fuzzy neural network model has already been used to solve these demands [12]. However, this paper presents the first neuro-fuzzy model to solve problems and extract advantageous interpretations of the dataset.

The paper is organized as follows: In Section 2, the literature supplies details about evolving fuzzy neural networks, interpretability of evolving fuzzy systems, and auction

fraud. Section 3 presents the model employed in this paper, highlighting its layers, training method, and interpretability criteria applied in the model's results. Section 4 presents the test features, the state-of-the-art model to reveal auction fraud, and the results acquired with due arguments and interpretation. Finally, Section 6 highlights the paper's conclusions and possible future work.

## **2. Literature Review**

#### *2.1. Artificial Neural Network and Applications*

Artificial neural networks (ANN) are mathematical models that can learn through computational means and are based on human networks of biological neurons. These networks process information using storage and processing structures, with each processor element representing a neuron. They are fed a set of weighted inputs, and their output is obtained by applying an activation function to simulate the degree of stimulation of the biological neuron in order to obtain the responses [13]. According to Fausett and others [14], ANN is a set of computational procedures that provide a mathematical representation inspired by the neural composition of intelligent organisms and that gain knowledge through expertise, allowing tasks typically performed by reasonable beings to be performed in computational environments.

Neural networks are constructed of many interconnected processing units known as neurons. This method is based on the nature of the human brain and how learning and problem solving work. Weighted bonds called synapses connect artificial neurons. Each neuron receives multiple input signals and generates an output signal [13].

Since the 1980s, studies on neural networks have undergone significant evolution, and this area of research has become well-known, either because of the promising features introduced by neural network models or because of the general technological requirement of implementation that allows the audacious development of applications of architectures with parallel neural networks in dedicated hardware, thus acquiring excellent fulfillment of these systems (foremost to conventional methods). Deep neural networks represent the state of the art in neural network development (or Deep Learning) [15]. Where the behavior of variables is not purely known, ANNs are frequently employed to solve complicated issues. Their capacity to learn from examples and generalize the knowledge acquired, producing a nonlinear model, is one of their key properties, which greatly increases the effectiveness of their use in spatial analysis [13].

The selection of the optimum architecture is one of the most challenging aspects of using neural networks since it is experimental and takes a long time to complete. The procedure must be used in practice to evaluate multiple learning models as well as the many topology configurations a network might have to address a particular issue [13].

In two different ways, a neural network approximates the human brain: information is obtained through knowledge stages, and synaptic weights are employed to gather experience. The existing connection between neurons is referred to as a synapse. Values called synaptic weights are assigned to the connections. This demonstrates that artificial neural networks are made up of a succession of artificial (or virtual) neurons that are coupled to form a system of processing components. Their acknowledgments are determined by how the model's underlying structures are linked, and their parameters are predicted [13].

At least one hidden layer is required in ANNs. If the model has multiple hidden layers, each one is accountable for increasing its capacity. The ANN architecture is capable of executing activities that aid in producing model outputs. The neurons in the hidden layers can be activated using activation functions (e.g., Gaussian, triangular, sigmoidal, sine, and hyperbolic tangent). These activation functions are in charge of introducing the nonlinear aspect of the model's activities. Backpropagation or Gradient Descent [16], Extreme Learning Machine [10], and others are examples of training methods for updating model parameters. An example of an artificial neural network is shown in Figure 1.

**Figure 1.** Artificial neural network with five layers.

#### *2.2. Fuzzy Neural Network*

Fuzzy neural networks are based on the theory of fuzzy sets and are trained by learning algorithms derived from neural networks. Being able to unify in a model the generalization of parameters and the training capacity provided by artificial neural networks together with the interpretability characteristics of fuzzy systems [17], fuzzy neural networks can work to solve problems of different varieties, making it easier to find solutions for a parameter update in the smart models. By interpreting aspects of the user's database of the problem, they identify existing patterns that make up a set of fuzzy rules capable of transforming numerical information into linguistic contexts that can be interpreted by people who do not necessarily know the main techniques of artificial intelligence. Incorporating fuzzy logic into the neural network can alleviate the insufficiency of each technique, approaching them as more economical, robust, and simple to understand problems.

These models have multilayer architectures, commonly, the three-layer ones stand out, but there may be differences in their architecture. Fuzzy neural networks have also been used for the detection of Pulmonary Tuberculosis [18]. They are also present in the detection of COVID-19 cases from chest X-rays [19]. Most of the models listed above have differences in their architecture. Each of the functions of these layers incorporates the concepts of fuzzification–defuzzification systems and artificial neural networks. The first layer is the one that receives the input data, converting them into fuzzy logic neurons. Fuzzy versions of c-means, adaptive-network-based fuzzy inference systems, and cloud clustering are usually implemented [7]. These techniques usually have at least one hidden layer. In the training algorithms, models based on backpropagation, genetic and evolutionary models, and Extreme Learning Machines stand out [7]. A model with an optimized structure determines its architecture from the fuzzy neural network and an output layer, which is also known as the defuzzification layer.

The architecture of a fuzzy neural network can be expressed in layers, where each one is responsible for a function in the model. Figure 2 represents a fuzzy neural networks in layers where one is responsible for the fuzzification process, the other takes the aggregation of fuzzy neurons, and the last layer is responsible for the model outputs. Recent proposals for fuzzy neural networks have addressed time-series forecasting [20,21], harmonic suppression [22], autonomous vehicles [23], and breast cancer [24].

**Figure 2.** Example of a layered fuzzy neural network.

#### *2.3. Fuzzy Natural Logic*

Fuzzy natural logic (FNL) is a class of mathematical theories that includes evaluative expression theory, theory of fuzzy/linguistic IF–THEN rules, and approximate reasoning based on them. The theory of generalized fuzzy quantifiers and their syllogisms, models of natural human reasoning, are also highlighted. FNL aims to develop models of human thought whose most relevant feature is the use of natural language [25].

Many works have been proposed to explore this theory to facilitate the understanding of the results by its users. We highlight works that addressed the theory of intermediate quantifiers in FNL [26], forecasting in analogous time series [27], integration of probabilistic uncertainty to fuzzy systems [28], and interpretable rules with medical data [29], among others.
