Social networks have been recently employed as a source of information for event detection, with particular reference to road traffic congestions 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 to detect traffic events almost in real-time, often before online traffic news web sites. We employed the Support Vector Machine as classification model and we achieved an accuracy of 95.75% by solving a binary classification problem (traffic vs. non-traffic tweets). We were also able to discriminate if traffic is caused by an external event or not, by solving a multi-class classification problem, and obtaining an accuracy of 88.89%.

In this paper, we propose the use of a multiobjective evolutionary approach to generate a set of linguistic fuzzy-rulebased 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 twotuple 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 nondominated sorting genetic algorithm (NSGA-II) and an accuracydriven 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.Index Terms-Accuracy-interpretability tradeoff, fuzzy rulebased systems (FRBSs), linguistic two-tuple representation, multiobjective evolutionary algorithms (EAs).

In the last years, the numerous successful applications of fuzzy rule-based systems (FRBSs) to several different domains have produced a considerable interest in methods to generate FRBSs from data. Most of the methods proposed in the literature, however, focus on performance maximization and omit to consider FRBS comprehensibility. Only recently, the problem of finding the right trade-off between performance and comprehensibility, in spite of the original nature of fuzzy logic, has arisen a growing interest in methods which take both the aspects into account. In this paper, we propose a Pareto-based multi-objective evolutionary approach to generate a set of Mamdani fuzzy systems from numerical data. We adopt a variant of the well-known (2+2) Pareto Archived Evolutionary Strategy ((2+2)PAES), which adopts the one-point crossover and two appropriately defined mutation operators. (2+2)PAES determines an approximation of the optimal Pareto front by concurrently minimizing the root mean squared error and the complexity. Complexity is measured as sum of the conditions which compose the antecedents of the rules included in the FRBS. Thus, low values of complexity correspond to Mamdani fuzzy systems characterized by a low number of rules and a low number of input variables really used in each rule. This ensures a high comprehensibility of the systems. We tested our version of (2+2)PAES on three well-known regression benchmarks, namely the Box and Jenkins Gas Furnace, the Mackey-Glass chaotic time series and Lorenz attractor time series datasets. To show the good characteristics of our approach, we compare the Pareto fronts produced by the (2+2)PAES with the ones obtained by applying a heuristic approach based on SVD-QR decomposition and four different multi-objective evolutionary algorithms.

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Context adaptation (CA) based on evolutionary algorithms is certainly a promising approach to the development of fuzzy rule-based systems (FRBSs). In CA, a context-free model is instantiated to a context-adapted FRBS so as to increase accuracy. A typical requirement in CA is that the context-adapted system maintains the same interpretability as the context-free model, a challenging constraint given that accuracy and interpretability are often conflicting objectives. Furthermore, interpretability is difficult to quantify because of its very nature of being a qualitative concept. In this paper, we first introduce a novel index based on fuzzy ordering relations in order to provide a measure of interpretability. Then, we use the proposed index and the mean square error as goals of a multi-objective evolutionary algorithm aimed at generating a set of Pareto-optimum context-adapted Mamdani-type FRBSs with different trade-offs between accuracy and interpretability. CA is obtained through the use of specifically designed operators that adjust the universe of the input and output variables, and modify the core, the support and the shape of fuzzy sets characterizing the partitions of these universes. Finally, we show results obtained by using our approach on synthetic and real data sets