# Confidence-Based Voting for the Design of Interpretable Ensembles with Fuzzy Systems +
## 1 Introduction  
The development of modern classification systems in the area of computational intelligence has led to the wide application of the neural networks, decision trees and support vector machines in a variety of fields, including industry, financial sphere, medicine, engineering and social sciences. The fuzzy logic, and more precisely fuzzy classification systems, are one of the most important technologies for machine learning in cases where interpretable classifiers are required. However, every type of classification system has advantages and disadvantages; for example, the neural networks have high accuracy, but their low interpretability, while decision trees have problems with overfitting. The fuzzy systems are usually characterized by lower precision, but their advantage is that they are the \"white box\" classifier, i.e., their inference procedure is easily understood by experts. The idea to combine several data mining methods together to solve the classification, regression or clustering problem is not new, and it is usually based on some implementation of voting. The advantage of voting is that it usually leads to increased generalization, so that higher accuracies are achieved on the test sets, and therefore in the real-world scenarios. For classification problems the easiest way to create an ensemble is to use the voting by majority. However, there are other ensemble design schemes, which include, but are not limited to bagging [1], boosting, [2; 3; 4], random forest [5], stacking [6]. Theboosting algorithms include: Adaboost [7], gradient boosting [8] and random subspace method [9]. In the most efficient algorithms for ensemble generation the weighting schemes are used. Several recent studies were focused on creating efficient schemes of generating ensembles of classifiers. In [10] the novel misclassification diversity measure as well as the incremental layered classifier selection approach were proposed. In [11] the divide-and-conquer classifier ensemble learning algorithm is proposed, which uses many-objective problem formulation to create efficient heterogeneous ensembles. In [12] the extension of the random subspace method is proposed, called hybrid the adaptive ensemble learning. This methods introduces the new way to adapt the weights of classifiers to achieve better results with the ensemble. In [13] the novel ensemble learning algorithm is presented, which is capable of adjusting the weights of the ensemble according to current data stream. The algorithm penalizes incorrect classification and has instruments for changes detection, allowing to achieve good classification performance at every moment. This study is focused on the development of a novel weighting technique, which uses the membership values, returned together with the class number in most fuzzy classification systems. These membership values are used as confidence levels, and the confidence-based voting decides whether the fuzzy classifier should be used, or the other, supporting classifier. This idea was originally proposed in [14]. The main difference and advantage of the proposed approach is that unlike previously mentioned methods it concentrates on combining two classifiers, where the first one is the main, and the second is the assisting classifier. This inequality of classifier roles allows receiving more interpretable and accurate results. The experimental section contains tests on 11 problems presented at the KEEL datasets repository, as well as on data, collected by Doppler effect sensors by using non-contact vital sensing. The real-world data contained information about the person's emotional state during listening to music. The the paper is organized as follows: Section 2 describes the fuzzy classification method used, namely the hybrid evolutionary fuzzy classification algorithm, as well as other used classifiers applied in this study and the confidence-based voting procedure.