The development of autonomous robotic systems offers significant potential for performing complex tasks with precision and consistency. Recent advances in Artificial Intelligence (AI) have enabled more capable intelligent automation systems, addressing increasingly complex challenges. However, this progress raises questions about human roles in such systems. Human-Centered AI (HCAI) aims to balance human control and automation, ensuring performance enhancement while maintaining creativity, mastery, and responsibility. For real-world applications, autonomous robots must balance task performance with reliability, safety, and trustworthiness. Integrating HCAI principles enhances human-robot collaboration and ensures responsible operation.This paper presents a bibliometric analysis of intelligent autonomous robotic systems, utilizing SciMAT and VOSViewer to examine data from the Scopus database. The findings highlight academic trends, emerging topics, and AI’s role in self-adaptive robotic behaviour, with an emphasis on HCAI architecture. These insights are then projected onto the IBM MAPE-K architecture, with the goal of identifying how these research results map into actual robotic autonomous systems development efforts for real-world scenarios.

The decentralized nature of federated learning (FL) poses critical challenges related to security: Clients participating in the process may not necessarily be trustworthy and could engage in adversarial attacks, potentially undermining the integrity and reliability of the global machine learning model. Security concerns have been extensively investigated in traditional FL, where collaboratively learned models are typically deep neural networks. However, this class of models does not meet the requirement of explainability, which is considered essential for the trustworthiness of AI systems. In this work, we present an analysis on security threats to FL of explainable models, namely fuzzy rule-based classifiers (FRBCs). We outline the types of attacks a malicious client may implement, and assess, through a preliminary experimental analysis, the impact they have on FL of FRBCs in terms of global model performance. We also compare these findings with the effects of the same or similar well-established attacks in traditional FL of neural network models. Finally, we provide insights to improve the security of FRBCs learned in a federated fashion.

The increasing complexity of cyber threats has necessitated the adoption of Intrusion Detection Systems (IDSs) which often rely on Artificial Intelligence (AI) models to detect malicious activities in network traffic. In distributed environments, interconnected private sub-networks pose additional challenges, as threats can spread while evading local detection. However, the use of AI models in these systems raises issues related to transparency, privacy, and data security. In this context, this study proposes a decentralized IDS based on Federated Learning (FL) and Explainable Artificial Intelligence (XAI) techniques. The network traffic classification model is based on a Multi-Layer Perceptron (MLP) neural network, while the SHapley Additive exPlanations (SHAP) method is employed to provide interpretable explanations of the system decisions. Fed-SHAP, based on the federated fuzzy c-means clustering, is used to generate a global SHAP background dataset to be adopted for generating consistent and reliable explanations. The system is evaluated on realistic scenarios with non-Independent and Identically Distributed (IID) network data. Experimental results demonstrate that the proposed federated approach maintains comparable accuracy with respect to centralized models while ensuring data protection and explanation consistency in federated environments.

The use of personal protective equipment (PPE) is essential to improve workplace safety. Despite specific regulations requiring the use of PPE, workers often neglect to wear it due to factors such as inattention, urgency, or convenience. Monitoring the correct use of PPE is especially critical in high-risk tasks. Computer vision technology can automate this process, leveraging deep neural models. This study investigates the performance of modern object detection models in identifying the correct use of PPE, focusing on their accuracy and execution speed. Specifically, the YOLOv11 and RT-DERT models are employed, trained on a real-world PPE dataset. Deployment on low-cost hardware, specifically an NVIDIA Jetson Nano, is evaluated using three deployment frameworks, namely PyTorch, OpenVINO, and TensorRT. The results show that YOLOv11n, with 2.6 million parameters, provides slightly lower average accuracy than more complex models. It stands out for its speed, reaching performances of 6.6 Frames Per Second (FPS) with PyTorch, 2.3 FPS with OpenVINO, and 10.6 FPS with TensorRT. On the other hand, YOLOv11l and YOLOv11x with, respectively, 46.5 and 86.7 million parameters offer higher accuracy, especially evident in small class identification, where simpler models tend to struggle. However, they show lower throughput, with 1.2 and 0.7 FPS on PyTorch. RT-DETR has competitive accuracy but lower performance on edge devices.

The emergence of 6G networks demands environment-aware communication paradigms to ensure reliable and efficient connectivity, and Channel Knowledge Maps (CKMs) offer a promising solution by mapping spatial locations to detailed channel characteristics for proactive network optimization. In this context, this paper proposes an explainable Machine Learning (ML)-based framework that uses geometrical features to predict receiver state probabilities in UAV-based mmWave communication networks. Geometrical characteristics extracted from the environment surrounding each receiver are used to train ML models, namely Decision Tree (DT), K-Nearest Neighbors (KNN), and Deep Neural Network (DNN) models, to predict three receiver states probabilities: Line-of-Sight (LOS), No-Line-of-Sight (NLOS), and Blocked. Experimental results show that the DNN model outperforms DT and KNN, achieving higher accuracy across all states, albeit with no inherent explainability. To address this, the SHapley Additive exPlanations (SHAP) method is applied to indicate feature contributions to each state prediction of the black-box DNN model. This improves the interpretability and reliability of the proposed environment-aware framework for$\mathbf{6 G}$UAV-based networks.

The use of personal protective equipment (PPE) is essential to strengthen the safety of workers in the workplace. Although there exist specific regulations requiring the use of PPEs, due to carelessness, haste or comfort, workers sometimes neglect to wear them. Thus, it is crucial to monitor the appropriate use of PPE, especially in dangerous processes. Computer vision technology can help perform this task automatically, exploiting appropriate deep neural models for recognizing PPE. YOLO (You Only Look Once) deep neural models ensure good accuracy against a limited complexity, which allows running them on devices with limited computational capacity. In this paper, we evaluate the performances, in terms of accuracy and processing speed, of the most popular models implemented in the version 5 of YOLO (YOLOv5) in the task of recognizing whether workers correctly wear PPE. To this aim, all models are trained on a PPE dataset on a dedicated server. Then, each model is deployed on low-cost hardware, which includes a Raspberry Pi4 Model B equipped with an Intel Neural Compute Stick 2, used as a processing unit. The outcomes show that YOLOv5n, with only 1.9 million parameters, is the fastest model which allows processing 7.9 frames per second, while YOLOv5l and YOLOv5x, respectively with 46.5 and 86.7 million parameters, are the most accurate but slowest models, processing 1.3 and 0.7 frames per second. We also compare the performance of the YOLOv5 models with the ones in version 4 of YOLO, showing how models in version 5 in general outperform the previous version with higher accuracy, especially in the detection of small objects.

Fuzzy Regression Trees (FRTs) are widely acknowledged as highly interpretable ML models, capable of dealing with noise and/or uncertainty thanks to the adoption of fuzziness. The accuracy of FRTs, however, strongly depends on the polynomial function adopted in the leaf nodes. Indeed, their modelling capability increases with the order of the polynomial, even if at the cost of greater complexity and reduced interpretability. In this paper we introduce the concept of Heterogeneous FRT: the order of the polynomial function is selected on each leaf node and can lead either to a zero-order or a first-order approximation. In our experimental assessment, the percentage of the two approximation orders is varied to cover the whole spectrum from pure zero-order to pure first-order FRTs, thus allowing an in-depth analysis of the trade-off between accuracy and interpretability. We present and discuss the results in terms of accuracy and interpretability obtained by the corresponding FRTs on nine benchmark datasets

The quest for trustworthiness in Artificial Intelligence (AI) is increasingly urgent, especially in the field of next-generation wireless networks. Future Beyond 5G (B5G)/6G networks will connect a huge amount of devices and will offer innovative services empowered with AI and Machine Learning tools. Nevertheless, private user data, which are essential for training such services, are not an asset that can be unrestrictedly shared over the network, mainly because of privacy concerns. To overcome this issue, Federated Learning (FL) has recently been proposed as a paradigm to enable collaborative model training among multiple parties, without any disclosure of private raw data. However, the initiative to natively integrate FL services into mobile networks is still far from being accomplished. In this paper we propose a novel FL-as-a-Service framework that provides the B5G/6G network with flexible mechanisms to allow end users to exploit FL services, and we describe its applicability to a Quality of Experience (QoE) forecasting service based on a vehicular networking use case. Specifically, we show how FL of eXplainable AI (XAI) models can be leveraged for the QoE forecasting task, and induces a benefit in terms of both accuracy, compared to local learning, and trustworthiness, thanks to the adoption of inherently interpretable models. Such considerations are supported by an extensive experimental analysis on a publicly available simulated dataset. Finally, we assessed how the learning process is affected by the system deployment and the performance of the underlying communication and computation infrastructure, through system-level simulations, which show the benefits of deploying the proposed framework in edge-based environments.

Federated Learning (FL) has been proposed as a privacy preserving paradigm for collaboratively training AI models: in an FL scenario data owners learn a shared model by aggregating locally-computed partial models, with no need to share their raw data with other parties. Although FL is today extensively studied, a few works have discussed federated approaches to generate explainable AI (XAI) models. In this context, we propose an FL approach to learn Takagi-Sugeno-Kang Fuzzy Rule-based Systems (TSK-FRBSs), which can be considered as XAI models in regression problems. In particular, a number of independent data owner nodes participate in the learning process, where each of them generates its own local TSK-FRBS by exploiting an ad-hoc defined procedure. Then, these models are forwarded to a server that is responsible for aggregating them and generating a global TSK-FRBS, which is sent back to the nodes. An appropriate aggregation strategy is proposed to preserve the explainability of the global TSK-FRBS. A thorough experimental analysis highlights that the proposed approach brings benefits, in terms of accuracy, to data owners participating in the federation preserving the privacy of the data. Indeed, the accuracy achieved by the global TSK-FRBS is higher than the ones of the TSK-FRBSs learned by exploiting only local training data.

Regression Trees (RTs) have been widely used in the last decades in various domains, also thanks to their inherent explainability. Fuzzy RTs (FRTs) extend RTs by using fuzzy sets and have proven to be particularly suitable for dealing with noisy and/or uncertain environments. The modelling capability of FRTs depends, among other factors, on the model used in the leaves for determining the output, and on the inference strategy. Nevertheless, the impact of such factors on FRTs accuracy and explainability has not been adequately investigated.In this paper, we extend a recently proposed learning scheme for FRTs by employing both linear models in the leaves and the maximum matching inference strategy. The former extension aims to increase accuracy, and the latter to improve explainability. We carried out an extensive experimental analysis by comparing the four FRT versions corresponding to any possible combination of the two extensions introduced in the paper. The results show that the best trade-off between accuracy and explainability is obtained by employing both of them.

In the last years, there has been an ever-increasing interest in profiling various aspects of city life, especially in the context of smart cities. This interest has become even more relevant recently when we have realized how dramatic events, such as the Covid-19 pandemic, can deeply affect the city life, producing drastic changes. Identifying and analyzing such changes, both at the city level and within single neighborhoods, may be a fundamental tool to better manage the current situation and provide sound strategies for future planning. Furthermore, such fine-grained and up-to-date characterization can represent a valuable asset for other tools and services, e.g., web mapping applications or real estate agency platforms. In this article, we propose a framework featuring a novel methodology to model and track changes in areas of the city by extracting information from online newspaper articles. The problem of uncovering clusters of news at specific times is tackled by means of the joint use of state-of-the-art language models to represent the articles, and of a density-based streaming clustering algorithm, properly shaped to deal with high-dimensional text embeddings. Furthermore, we propose a method to automatically label the obtained clusters in a semantically meaningful way, and we introduce a set of metrics aimed at tracking the temporal evolution of clusters. A case study focusing on the city of Rome during the Covid-19 pandemic is illustrated and discussed to evaluate the effectiveness of the proposed approach.

The increasing number of always more sophisticated car sensors, which allow to extract information about the driver, encourages auto vehicle developers and researchers to focus on the topic of driver identification. The advantages can be various, such as to customise and improve driver experience, to increase safety and to reduce global environmental problems. This work explores a set of features extracted from a car monitoring system, installed on real cars, to identify the driver on the basis of his/her driving behaviour. The proposed features are leveraged by a Multiobjective Evolutionary Learning Scheme for generating Fuzzy Rule-Based Classifiers characterized by different trade-offs between the classification accuracy and the explainability of the classification models. To evaluate the effectiveness and efficiency of the proposed approach, we carry out an experimental analysis on a real-world dataset, composed by actual measures extracted from 4 cars driven by 4 different drivers. The results show that the fuzzy classification models experimented in this work are more accurate and explaninable than the classification models generated adopting tree-based classifiers, such as decision trees and random forests.

Explainable Artificial Intelligence (XAI) is expected to play a key role in the design phase of next generation cellular networks. As 5G is being implemented and 6G is just in the conceptualization stage, it is increasingly clear that AI will be essential to manage the ever-growing complexity of the network. However, AI models will not only be required to deliver high levels of performance, but also high levels of explainability. In this paper we show how fuzzy models may be well suited to address this challenge. We compare fuzzy and classical decision tree models with a Random Forest (RF) classifier on a Quality of Experience classification dataset. The comparison suggests that, in our setting, fuzzy decision trees are easier to interpret and perform comparably or even better than classical ones in identifying stall events in a video streaming application. The accuracy drop with respect to RF classifier, which is considered to be a black-box ensemble model, is counterbalanced by a significant gain in terms of explainability.

Tracking and profiling changes in the occurrence of notable events in a city, in terms of what happens in the different areas and how possible changes are perceived, is an important issue in the context of smart cities: in fact, it may be helpful in developing applications to help administrations and citizens alike. In this paper, we propose an approach to provide time-sensitive snapshots of events within the different areas of a city, and the city as a whole. To probe inside neighborhoods and communities, we propose to use articles in online newspapers, as they represent an accessible source of information on what notable events actually happen, and on the most relevant topics at a given moment in time. We adopt an approach to group up articles by means of clustering, and to automatically assign labels to clusters by analyzing their content. The outcomes of this procedure, repeated along a certain timespan, are able to describe the temporal evolution of notable events in specific city areas. In this paper we show the effectiveness of the proposed methodology by reporting a case study for the city of Rome, over an investigation span of few years, which includes also the Covid-19 pandemic period.

The adoption of real-time object detection systems via video streaming analysis is currently exploited in several contexts, from security monitoring to safety prevention. In industrial environments, proper usage of Personal Protective Equipment (PPE) is paramount to ensure workers’ safety. However, the use of some types of PPE, such as helmets, is often neglected by workers, especially in indoor areas. Thus, in order to reduce the risks of accidents, real-time video streaming-based monitoring systems may be used to monitor areas in which workers operate and alert them not to wear PPEs via acoustic alarms or visual signals. In case of a remote analysis, there are potential issues related to the high rate of data streams to be transported and analyzed and workers’ privacy. In this work, we propose an embedded smart system for real-time PPE detection based on video streaming analysis and deep learning models. We discuss the deployment of different versions of the YOLOv4 network fine-tuned using a public PPE dataset. In the end, we assess the performance of the proposed system in terms of accuracy and latency and of the overall PPE detection procedure.

Fairness, Accountability, Transparency and Explainability have become strong requirements in most practical applications of Artificial Intelligence (AI). Fuzzy sets and systems are recognized world-wide because of their outstanding contribution to model AI systems with a good interpretability-accuracy trade-off. Accordingly, fuzzy sets and systems are at the core of the so-called Explainable AI. ExpliClas is a software as a service which paves the way for interpretable and self-explainable intelligent systems. Namely, this software provides users with both graphical visualizations and textual explanations associated with intelligent classifiers automatically learned from data. This paper presents the new functionality of ExpliClas regarding the generation, evaluation and explanation of fuzzy decision trees along with fuzzy inference-grams. This new functionality is validated with two well-known classification datasets (i.e., Wine and Pima), but also with a real-world beer-style classifier.

Density-based clustering algorithms represent a convenient approach when the number of clusters is not known in advance and their shapes are arbitrary. Nevertheless, they are highly sensitive to the input parameter setting, especially when clusters' borders are close to each other, or even overlap. In this paper we propose FDBSCAN-APT, a fuzzy extension of the DBSCAN algorithm. FDBSCAN-APT is able to discover clusters with fuzzy overlapping borders and relies on the automatic setting of input parameters thanks to the definition of a novel heuristic based on the statistical modelling of the density distribution of objects. An extensive experimental analysis carried out on synthetic datasets shows that FDBSCAN-APT always finds reasonable parameter configurations and produces good clustering results in a variety of challenging scenarios.

The paper presents a framework for characterizing and profiling city areas from available data provided by online web services and web sites. These data are points of interest (restaurants, services, hotels, schools, churches, shops, wi-fi access points, etc.) disseminated in the city, local news, traffic information, city events, lifestyle and human behaviors. The framework allows selecting the different data sources, preprocessing the data, extracting meaningful features, executing a clustering algorithm to determine the profiles of the single areas of the city, and visualizing the results on the city map. The definition of the areas is based on the construction of a virtual grid of squared cells on the city. We employed the framework for profiling areas of the metropolitan city of Milan, Italy. We tested different cell sizes and employed the k-means clustering algorithm to group similar areas of the city. We highlight how areas belonging to the same cluster, although located in different zones of the city, actually present similar characteristics. Such a framework can be of the utmost importance for several entities. By exploiting the profiles of the city areas, citizens can benefit from tailored services, enterprises can define ad hoc marketing strategies, and local governments can be supported in decision making.

Fuzzy associative classification has not been widely analyzed in the literature, although associative classifiers (ACs) have proved to be very effective in different real domain applications. The main reason is that learning fuzzy ACs is a very heavy task, especially when dealing with large datasets. To overcome this drawback, in this paper, we propose an efficient distributed fuzzy associative classification approach based on the MapReduce paradigm. The approach exploits a novel distributed discretizer based on fuzzy entropy for efficiently generating fuzzy partitions of the attributes. Then, a set of candidate fuzzy association rules is generated by employing a distributed fuzzy extension of the well-known FP-Growth algorithm. Finally, this set is pruned by using three purposely adapted types of pruning. We implemented our approach on the popular Hadoop framework. Hadoop allows distributing storage and processing of very large data sets on computer clusters built from commodity hardware. We have performed an extensive experimentation and a detailed analysis of the results using six very large datasets with up to 11 000 000 instances. We have also experimented different types of reasoning methods. Focusing on accuracy, model complexity, computation time, and scalability, we compare the results achieved by our approach with those obtained by two distributed nonfuzzy ACs recently proposed in the literature. We highlight that, although the accuracies result to be comparable, the complexity, evaluated in terms of number of rules, of the classifiers generated by the fuzzy distributed approach is lower than the one of the nonfuzzy classifiers.

One of the primary constraints in the design and deployment of WSNs is energy, as sensor nodes are powered by batteries. In such networks, energy efficiency can be achieved by reducing the use of the onboard radios, for instance, limiting packet transmissions. The broadcast nature of the wireless channel surely represents an advantage in this respect: each node has to send a single broadcast packet to simultaneously reach all its neighboring nodes, thus reducing the number of required transmissions. We present an integrated optimization framework leveraging on this advantage to improve the convergence speed of a distributed consensus algorithm, by means of topology design. We evaluate the effectiveness of the proposed framework in terms of overall energy savings and worst case algorithmic complexity of the optimization task, on different classes of network topologies, and compare such results with those obtained by a pure greedy strategy recently proposed in the literature. We prove that our framework can slightly reduce the average nodes' energy cost with respect to its greedy antagonist, as well as reducing the computational overhead of the optimization task to a small fraction of the latter. These unique features make it suitable to tackle the problem also over large scenarios.

In this paper, we analyze and compare four multi-objective evolutionary granular rule-based classifiers. We learn concurrently the rule base, the most suitable number of granules and their parameters during the evolutionary process. Rule learning is performed by a method, which selects rules and conditions from an initial heuristically-generated rule base. The four classifiers differ for the type of granule, namely Type-1 and Type-2 fuzzy sets, and for the method used for generating the initial rule base, namely crisp and fuzzy decision tree learning algorithms. Results show that generating the initial rule base by using a fuzzy decision tree outperforms the use of the crisp decision tree. On the other hand, no statistical difference exists between the use of Type-1 and Type-2 fuzzy sets as granules.

Internet traffic classification has moved in the last years from traditional port and payload-based approaches towards methods employing statistical measurements and machine learning techniques. Despite the success achieved by these techniques, they are not able to explain the relation between the features, which describe the traffic flow, and the corresponding traffic classes. This relation can be extremely useful to network managers for quickly handling possible network drawback. In this paper, we propose to tackle the traffic classification problem by using multi-objective evolutionary fuzzy classifiers (MOEFCs). MOEFCs are characterised by good trade-offs between accuracy and interpretability. We adopt two Internet traffic datasets extracted from two real-world networks. We discuss the results obtained both by applying a cross validation on each single dataset, and by using a dataset as training set and the other as test set. We show that, in both cases, MOEFCs can achieve satisfactory accuracy in the face of low complexity and, therefore, high interpretability.

In this paper, we propose an efficient distributed fuzzy associative classification model based on the MapReduce paradigm. The learning algorithm first mines a set of fuzzy association classification rules by employing a distributed version of a fuzzy extension of the well-known FP-Growth algorithm. Then, it prunes this set by using three purposely adapted types of pruning. We implemented the distributed fuzzy associative classifier using the Hadoop framework. We show the scalability of our approach by carrying out a number of experiments on a real-world big dataset. In particular, we evaluate the achievable speedup on a small computer cluster, highlighting that the proposed approach allows handling big datasets even with modest hardware support.

Social networks have been recently employed as a source of information for event detection, with particular reference to road traffic congestion and car accidents. In this paper, we present a real-time monitoring system for traffic event detection from Twitter stream analysis. The system fetches tweets from Twitter according to several search criteria; processes tweets, by applying text mining techniques; and finally performs the classification of tweets. The aim is to assign the appropriate class label to each tweet, as related to a traffic event or not. The traffic detection system was employed for real-time monitoring of several areas of the Italian road network, allowing for detection of traffic events almost in real time, often before online traffic news web sites. We employed the support vector machine as a classification model, and we achieved an accuracy value of 95.75% by solving a binary classification problem (traffic versus nontraffic tweets). We were also able to discriminate if traffic is caused by an external event or not, by solving a multiclass classification problem and obtaining an accuracy value of 88.89%.

Recent studies have highlighted that a significant part of the electrical energy consumption in residential buildings is caused by an improper use of home appliances. The development of low-cost systems for profiling the consumption of electric appliances can play a key role in stimulating the users to adopt adequate policies for energy saving. In this paper, we describe a novel methodology for extracting the power consumption of each appliance deployed in a domestic environment from the aggregate measures collected by a single smart meter. In order to coarsely describe how each type of appliance works, we use finite-state machines (FSMs) based on fuzzy transitions. An ad-hoc disaggregation algorithm exploits a database of these FSMs for, at each meaningful variation in real and reactive aggregate powers, hypothesizing possible configurations of active appliances. This set of configurations is concurrently managed by the algorithm which, whenever requested, outputs the configuration with the highest confidence with respect to the sequence of detected events. We implemented a prototype of a monitoring system based on the proposed methodology and installed it in a real domestic scenario. We discuss an experiment in which 11 appliances were connected to the same circuit and the aggregate power consumption was measured by a smart meter for approximately 12 h. At the end of the experiment, only two possible configurations were outputs from the system, including the correct one.

In this paper, we exploit a multi-objective evolutionary algorithm (MOEA) to generate fuzzy rule-based classifiers (FRBCs) with different trade-offs between classification accuracy and rule base complexity. In order to learn the rule base we employ a rule and condition selection (RCS) approach which aims to select a reduced number of rules from a heuristically generated rule base and concurrently a reduced number of conditions for each selected rule. During the multi-objective evolutionary process, we generate the rule bases of the FRBCs by the RCS approach and concurrently learn the membership function parameters of the linguistic values used in the rules. The MOEA has been tested on fifteen classification benchmarks and compared with a similar technique proposed recently in the literature. We show how the FRBCs generated by our approach can achieve considerable accuracies, despite a low rule base complexity.

When dealing with datasets that are characterized by a large number of instances, multiobjective evolutionary learning (MOEL) of fuzzy rule-based systems (FRBSs) suffers from high computational costs, mainly because of the fitness evaluation. The use of a reduced set of representative instances in place of the overall training set (TS) would considerably lessen the computational effort. Even though a large number of papers have proposed instance selection approaches, mainly in classification problems, how this selection should be performed, especially in the context of regression, is still an open issue. In this paper, we tackle the instance selection problem in the framework of MOEL of FRBSs through a coevolutionary approach. In the execution of the MOEL, periodically, a single-objective genetic algorithm (SOGA) evolves a population of reduced TSs. The SOGA aims to maximize a purposely defined index which measures how much the Pareto fronts computed by using, respectively, the reduced TS and the overall TS are close to each other: The closer the fronts, the more the reduced TS is representative of the overall TS. During the execution of the MOEL, the rule base and the membership function parameters of the fuzzy sets are concurrently learned by maximizing the accuracy and minimizing the complexity. We tested our approach on 12 large datasets. We adopted reduced TSs composed of 5%, 10%, and 20% of the overall TS. Using nonparametric statistical tests, we verified that with 10% and 20% of the overall TS, the Pareto front approximations that are generated by our coevolutionary approach are comparable with the ones generated by applying the MOEL with the overall TS, although the coevolution allows us to save up to 86.36% of the execution time. In addition, the analysis of the behavior of three representative solutions on the test set highlights that the use of the reduced TSs does not affect the generalization capabilities of the generated FRBSs.

In the framework of multi-objective evolutionary fuzzy systems (MOEFSs), the search space grows as the number of features of the dataset increases, leading to a slow and possibly difficult convergence of the evolutionary algorithm. Furthermore, mainly due to the fitness evaluation, datasets with a large number of instances require very high computational costs. In this paper, we propose a co-evolutionary approach to generate sets of Mamdani fuzzy rule-based systems (MFRBSs) with different trade-offs between accuracy and interpretability. We aim to deal with high dimensional and large datasets and to learn together the rule base (RB) and the membership function parameters. To reduce the search space, we perform the multi-objective evolutionary learning of the RB by selecting reduced sets of rules and conditions from a previously generated RB. Further, to lessen the computational costs, during the multi-objective evolutionary learning process, periodically, a single-objective genetic algorithm evolves a population of reduced training sets. We show the preliminary results obtained by applying our approach to two real world high dimensional and large regression datasets.

In this work, an intelligent system for automatic detection of fault in PV fields is proposed. This system is based on a Takagi-Sugeno-Kahn Fuzzy Rule-Based System (TSK-FRBS), which provides an estimation of the instant power production of the PV field in normal functioning, i.e, when no faults occur. Then, the estimated power is compared with the real power and an alarm signal is generated if the difference between powers overcomes a threshold. The TSK-FRBS has been trained using data collected from a PV plant simulator, during normal functioning. Preliminary tests were carried out in a simulated framework, by reproducing both normal and fault conditions. Results show that the system can recognize more than 90% of fault conditions, even when noisy data are introduced.

In this paper, we propose a three-objective evolutionary algorithm to generate a set of Mamdani fuzzy rule-based systems (MFRBSs) with different tradeoffs between accuracy, rule base (RB) complexity and partition integrity. The RB, the linguistic partition granularities and the membership function (MF) parameters are concurrently learnt during the evolutionary process. In particular, the granularity learning is performed by exploiting the concept of virtual RB and an appropriate mapping strategy, and the MF parameter tuning is achieved by a piecewise linear transformation. The RB complexity is measured as the total number of conditions in the antecedents of the rules and the partition integrity is evaluated by using a purposely-defined index, based on the piecewise linear transformation. We use a chromosome composed of three parts, which codify, respectively, the RB, and, for each variable, the number of fuzzy sets and the parameters of the piecewise linear transformation of the membership functions. Results on two real-world regression problems are shown and discussed.

When applied to high dimensional datasets, multi-objective evolutionary learning (MOEL) of fuzzy rule-based systems suffers from high computational costs, mainly due to the fitness evaluation. To use a reduced training set (TS) in place of the overall TS could considerably lessen the required effort. How this reduction should be performed, especially in the context of regression, is still an open issue. In this paper, we propose to adopt a co-evolutionary approach. In the execution of the MOEL, periodically, a single-objective genetic algorithm (SOGA) evolves a population of reduced TSs. The SOGA aims to maximize a purposely-defined index which measures how much a reduced TS is representative of the overall TS in the context of the MOEL. We tested our approach on a real world high dimensional dataset. We show that the Pareto fronts generated by applying the MOEL with the overall and the reduced TSs are comparable, although the use of the reduced TS allows saving on average the 75% of the execution time.

In this paper, we introduce a new index for evaluating the interpretability of Mamdani fuzzy rule-based systems (MFRBSs). The index takes both the rule base complexity and the data base integrity into account. We discuss the use of this index in the multi-objective evolutionary generation of MFRBSs with different trade-offs between accuracy and interpretability. The rule base and the membership function parameters of the MFRBSs are learnt concurrently by exploiting an appropriate chromosome coding and purposely-defined genetic operators. Results on a real-world regression problem are shown and discussed.

In this paper, we propose a novel approach to system identification based on morphogenetic theory (MT). Given a context H defined by a set of M objects, each described by a set of N attributes, and a vector X of desired outputs for each object, MT combines notions from formal concept analysis and tensor calculus so as to generate a morphogenetic system (MS). The MS is defined by a set of weights s1, …, sN, one for each attribute. Given H and X, weights are computed so as to generate the projection Y of X on the space of the attributes with the minimum distance between Y and X. An MS can be represented as a neuron, morphogenetic neuron, with a number of synapses equal to the number of attributes and synaptic weights equal to s1, …, sN. Unlike traditional neural network paradigm, which adopts an iterative process to determine synaptic weights, in MT, weights are computed at once. We introduce a method to generate a morphogenetic neural network (MNN) for identification problems. The method is based on extending appropriately and iteratively the attribute space so as to reduce the error between desired output and computed output. By using four well-known datasets, we show that an MNN can identify an unknown system with a precision comparable with classical multilayer perceptron with complexity similar to the MNN but reducing drastically the time needed to generate the neural network. Furthermore, the structure of the MNN is generated automatically by the method and does not require a trial-and-error approach often applied in classical neural networks. © 2009 Wiley Periodicals, Inc.

In this paper, we propose the use of a multiobjective evolutionary approach to generate a set of linguistic fuzzy-rule-based systems with different tradeoffs between accuracy and interpretability in regression problems. Accuracy and interpretability are measured in terms of approximation error and rule base (RB) complexity, respectively. The proposed approach is based on concurrently learning RBs and parameters of the membership functions of the associated linguistic labels. To manage the size of the search space, we have integrated the linguistic two-tuple representation model, which allows the symbolic translation of a label by only considering one parameter, with an efficient modification of the well-known (2$+$2) Pareto Archived Evolution Strategy (PAES). We tested our approach on nine real-world datasets of different sizes and with different numbers of variables. Besides the (2$+$2)PAES, we have also used the well-known non-dominated sorting genetic algorithm (NSGA-II) and an accuracy-driven single-objective evolutionary algorithm (EA). We employed these optimization techniques both to concurrently learn rules and parameters and to learn only rules. We compared the different approaches by applying a nonparametric statistical test for pairwise comparisons, thus taking into consideration three representative points from the obtained Pareto fronts in the case of the multiobjective EAs. Finally, a data-complexity measure, which is typically used in pattern recognition to evaluate the data density in terms of average number of patterns per variable, has been introduced to characterize regression problems. Results confirm the effectiveness of our approach, particularly for (possibly high-dimensional) datasets with high values of the complexity metric.

In this paper we propose a multi-objective genetic algorithm to generate Mamdani fuzzy rule-based systems with optimal trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we exploit a chromosome composed of two parts, which codify the numbers of fuzzy sets for each linguistic variable and the rule base, respectively. Rule bases defined on partitions with different granularity are handled by using an appropriate mapping strategy. The algorithm has been tested on a real word regression problem showing very promising results.

In this paper, we propose a novel population- based multi-objective evolutionary algorithm (MOEA) for binary classifier optimization. The two objectives considered in the proposed MOEA are the false positive rate (FPR) and the true positive rate (TPR), which are the two measures used in the ROC analysis to compare different classifiers. The main feature of our MOEA is that the population evolves based on the properties of the convex hulls defined in the FPR-TPR space. We discuss the application of our MOEA to determine a set of fuzzy rule-based classifiers with different trade-offs between FPR and TPR in lung nodule detection from CT scans. We show how the Pareto front approximation generated by our MOEA is better than the one generated by NSGA-II, one of the most known and used population-based MOEAs.

An approach to select the most suitable fuzzy rule-based binary classifier to a specific application is proposed. First, an evolutionary three-objective optimization algorithm is applied to generate an approximation of a Pareto front composed of fuzzy rule-based binary classifiers with different trade-offs between accuracy and complexity. Accuracy is measured in terms of sensitivity and specificity, whereas complexity is computed as sum of the conditions which compose the antecedents of the rules included in the classifiers. Thus, low values of complexity correspond to fuzzy systems characterized by a low number of rules and a low number of input variables actually used in each rule. This ensures a high comprehensibility of the classifiers. Then, the most suitable classifier is selected by using the ROC convex hull method. We discuss the application of the proposed approach to generate a classifier for discriminating lung nodules from non-nodules in a computer aided diagnosis (CAD) system. Results obtained on a real data set extracted from lung CT images are also discussed