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Abstract-Classification techniques are becoming essential in the financial world for reducing risks and possible disasters. Managers are interested in not only high accuracy but also in interpretability and transparency. It is widely accepted now that the comprehension of how inputs and output 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 towards the majority class. With the aim of achieving high accuracies, preserving the interpretability and managing uncertain and unbalanced data, the 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 multi-objective 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 eleven 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 fuzzy rule-based classifiers FARC-HD and FURIA, the classical C4.5 decision tree algorithm and its costsensitive version. Using non-parametric statistical tests, we will show that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable to 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...

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Abstract-Following the global economic crisis, many financial organisations around the World are seeking efficient frameworks for predicting and assessing financial risks. However, in the current economic situation, transparency became an important factor where there is a need to fully understand and analyse a given financial model. In this paper, we will present a Genetic Type-2 Fuzzy Logic System (FLS) for the modelling and prediction of financial applications. The proposed system is capable of generating summarized optimised type-2 FLSs based financial models which are easy to read and analyse by the lay user. The system is able to use the summarized model for prediction within financial applications. We have performed several evaluations in two distinctive financial domains one for the prediction of good/bad customers in a credit card approval application and the other domain was in the prediction of arbitrage opportunities in the stock markets. The proposed Genetic type-2 FLS has outperformed white box financial models like the Evolving Decision Rule (EDR) procedure (which is based on Genetic Programming (GP) and decision trees) and gave a comparable performance to black box models like neural networks while the proposed system provided a white box model which is easy to understand and analyse by the lay user.

Abstract-Today stock market exchange and finance are centers of attention all over the world. In finance, arbitrage is the practice of taking advantage of a price misalignment between two or more stock markets where profit can be earned by striking a combination of matching deals that capitalize upon the misalignment. If one strikes when misalignment has been observed, such deals are practically risk-free. However, when risk-free profit is around, everyone would compete to take advantage of it. Therefore, the question is whether arbitrage opportunities can be predicted; after all, misalignment does not happen instantaneously. Furthermore, financial operators do not like black boxes in forecasting. In this paper, we will present a type-2 Fuzzy Logic System (FLS) for the modeling and prediction of financial applications. The proposed system is capable of generating summarized models from pre-specified number of linguistic rules, which enables the user to understand the generated models for arbitrage opportunities prediction. The system is able to use this summarized model for the prediction of arbitrage opportunities in stock markets. We have performed several experiments based on the arbitrage data which is used in stock markets to spot ahead of time arbitrage opportunities. The proposed type-2 FLS has outperformed the Evolving Decision Rule (EDR) procedure (which is based on Genetic Programming (GP) and decision trees). Like GP, the type-2 FLS is capable of providing a white box model which could be easily understood and analyzed by the lay user.