Multiobjective Evolutionary Optimization of Type-2 Fuzzy Rule-Based Systems for Financial Data Classification

Classification techniques are becoming essential in the financial world for reducing risks and possible disasters. Managers are interested in not only high accuracy, but in interpretability and transparency as well. It is widely accepted now that the comprehension of how inputs and outputs are related to each other is crucial for taking operative and strategic decisions. Furthermore, inputs are often affected by contextual factors and characterized by a high level of uncertainty. In addition, financial data are usually highly skewed toward the majority class. With the aim of achieving high accuracies, preserving the interpretability, and managing uncertain and unbalanced data, this paper presents a novel method to deal with financial data classification by adopting type-2 fuzzy rule-based classifiers (FRBCs) generated from data by a multiobjective evolutionary algorithm (MOEA). The classifiers employ an approach, denoted as scaled dominance, for defining rule weights in such a way to help minority classes to be correctly classified. In particular, we have extended PAES-RCS, an MOEA-based approach to learn concurrently the rule and data bases of FRBCs, for managing both interval type-2 fuzzy sets and unbalanced datasets. To the best of our knowledge, this is the first work that generates type-2 FRBCs by concurrently maximizing accuracy and minimizing the number of rules and the rule length with the objective of producing interpretable models of real-world skewed and incomplete financial datasets. The rule bases are generated by exploiting a rule and condition selection (RCS) approach, which selects a reduced number of rules from a heuristically generated rule base and a reduced number of conditions for each selected rule during the evolutionary process. The weight associated with each rule is scaled by the scaled dominance approach on the fuzzy frequency of the output class, in order to give a higher weight to the minority class. As regards the data base learning, the membership function parameters of the interval type-2 fuzzy sets used in the rules are learned concurrently to the application of RCS. Unbalanced datasets are managed by using, in addition to complexity, selectivity and specificity as objectives of the MOEA rather than only the classification rate. We tested our approach, named IT2-PAES-RCS, on 11 financial datasets and compared our results with the ones obtained by the original PAES-RCS with three objectives and with and without scaled dominance, the FRBCs, fuzzy association rule-based classification model for high-dimensional dataset (FARC-HD) and fuzzy unordered rules induction algorithm (FURIA), the classical C4.5 decision tree algorithm, and its cost-sensitive version. Using nonparametric statistical tests, we will show that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable with and complexity lower than the ones generated by the two versions of the original PAES-RCS. Further, the FRBCs generated by FARC-HD and FURIA and the decision trees computed by C4.5 and its cost-sensitive version, despite the highest complexity, result to be less accurate than the FRBCs generated by IT2-PAES-RCS. Finally, we will highlight how these FRBCs are easily interpretable by showing and discussing one of them

Urban and social sensing for sustainable mobility in smart cities

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Delaying Inconsistency Resolution Using Fuzzy Logic

While developing complex systems, software engineers generally have to deal with various kinds of inconsistencies. Certain kinds of inconsistencies are inevitable, for instance, in case of multiple persons working independently of each other within the same project. Some inconsistencies are desirable when, for instance, alternative solutions exist for the same problem, and these solutions have to be preserved to allow further refinements along the development process. Current software development methods do not provide adequate means to model the desired inconsistencies and, therefore, aim to resolve the inconsistencies whenever they are detected. Although early resolution of inconsistencies reduces complexity of design by eliminating possible alternatives, it results in loss of information and excessive restriction of the design space. This paper aims to enhance the current methods by modelling and controlling the desired inconsistencies through the application of fuzzy logic

Feature Selection based on a Modified Fuzzy C-means Algorithm with Supervision

In this paper we propose a new approach to feature selection based on a modified fuzzy C-means algorithm with supervision (MFCMS). MFCMS completes the unsupervised learning of classical fuzzy C-means with labeled patterns. The labeled patterns allow MFCMS to accurately model the shape of each cluster and consequently to highlight the features which result to be particularly effective to characterize a cluster. These features are distinguished by a low variance of their values for the patterns with a high membership degree to the cluster. If, with respect to these features, the distance between the prototype of the cluster and the prototypes of the other clusters is high, then these features have the property of discriminating between the cluster and the other clusters. To take these two aspects into account, for each cluster and each feature, we introduce a purposely defined index: the higher the value of the index, the higher the discrimination capability of the feature for the cluster. We execute MFCMS on the training set considering all patterns as labeled. Then, we retain the features which are associated, at least for one cluster, with an index larger than a threshold τ. We applied MFCMS to several real-world pattern classification benchmarks. We used the well-known k-nearest neighbors as learning algorithm. We show that feature selection performed by MFCMS achieved an improvement in generalization on all data sets

k-NN algorithm based on Neural Similarity

The aim of this paper is to present a k-nearest neighbour (k-NN) classifier based on a neural model of the similarity measure between data. After a preliminary phase of supervised learning for similarity determination, we use the neural similarity measure to guide the k-NN rule. Experiments on both synthetic and real-world data show that the similarity-based k-NN rule outperforms the Euclidean distance-based k-NN rule

Enabling traceability in the wine supply chain

In the last decade, several factors have determined an increasing demand for wine supply chain transparency. Indeed, amalgamation, fraud, counterfeiting, use of hazardous treatment products and pollution are affecting the trust of consumers, who are more and more oriented to consider the so-called "credence attributes" rather than price. Thus, consumers demand detailed information on the overall process from the grape to the bottle. In this chapter, we present a system for traceability in the wine supply chain. The system is able to systematically store information about products and processes throughout the entire supply chain, from grape growers to retailers. Also, the system manages quality information, thus enabling an effective analysis of the supply chain processes

A Simple Algorithm for Data Compression in Wireless Sensor Networks

Power saving is a critical issue in wireless sensor networks (WSNs) since sensor nodes are powered by batteries which cannot be generally changed or recharged. As radio communication is often the main cause of energy consumption, extension of sensor node lifetime is generally achieved by reducing transmissions/receptions of data, for instance through data compression. Exploiting the natural correlation that exists in data typically collected by WSNs and the principles of entropy compression, in this Letter we propose a simple and efficient data compression algorithm particularly suited to be used on available commercial nodes of a WSN, where energy, memory and computational resources are very limited. Some experimental results and comparisons with, to the best of our knowledge, the only lossless compression algorithm previously proposed in the literature to be embedded in sensor nodes and with two well-known compression algorithms are shown and discussed

Some considerations on input and output partitions to produce meaningful conclusions in fuzzy inference

A large number of papers have been devoted to point out which combinations of the several fuzzy implication, composition and aggregation operators are necessary to satisfy a natural requirement for meaningful reasoning, that is, given a system observation which matches the antecedent of a rule, the conclusion of the inference process matches the consequent of that rule. Nevertheless, only few of these papers have analysed, once fixed a combination, which constraints on the reciprocal position of input and output fuzzy sets should be satisfied. In this paper, we consider fuzzy implication operators which are extensions of the two-valued logic implication operator and are non-decreasing with respect to their second argument, generic Sup-T composition operators, and minimum as aggregation operator. First, we analyse some features (namely, uniform level of indetermination, perfect matching with the consequent of a rule, and complete indetermination) of the conclusions inferred by those fuzzy implication operators with regard to fuzzy reasoning with one rule. Then, as regards approximate reasoning with multiple rules, we demonstrate that, if the fundamental requirement for fuzzy reasoning is satisfied, then the fuzzy sets which partition the input and output universes have to meet appropriate constraints. Finally, we provide a sufficient condition defined on input fuzzy sets to obtain a reasonable inference result