This paper concerns several important topics of the Symmetry journal, namely, pattern recognition, computer-aided design, diversity and similarity. We also take advantage of the symmetric and asymmetric structure of a transfer function, which is responsible to map a continuous search space to a binary search space. A new method for design of a fuzzy-rule-based classifier using metaheuristics called Gravitational Search Algorithm (GSA) is discussed. The paper identifies three basic stages of the classifier construction: feature selection, creating of a fuzzy rule base and optimization of the antecedent parameters of rules. At the first stage, several feature subsets are obtained by using the wrapper scheme on the basis of the binary GSA. Creating fuzzy rules is a serious challenge in designing the fuzzy-rule-based classifier in the presence of high-dimensional data. The classifier structure is formed by the rule base generation algorithm by using minimum and maximum feature values. The optimal fuzzy-rule-based parameters are extracted from the training data using the continuous GSA. The classifier performance is tested on real-world KEEL (Knowledge Extraction based on Evolutionary Learning) datasets. The results demonstrate that highly accurate classifiers could be constructed with relatively few fuzzy rules and features.

A method of using the shuffled frog leaping algorithm as a tool for expanding the primary base of fuzzy classifier rules is proposed. This algorithm is rel

Dynamic signature verification is one of the most fast, intuitive, and cost effective tools for user authentication. Dynamic signature recognition uses multiple characteristics in the analysis of an individual’s handwriting. Dynamic characteristics include the velocity, acceleration, timing, pressure, and direction of the signature strokes, all analyzed in the x, y, and z directions. In this paper, the constant term and the first seven harmonics of the Fourier series expansion of the signature were used as features. The authentication systems development includes the following stages: preprocessing, feature selection, classification. Binary metaheuristic algorithms and deterministic algorithms are used to select attributes. The classification was carried out using a fuzzy classifier. The fuzzy classifiers parameters were tuned using continuous metaheuristic algorithms. The efficiency of the authentication system was verified on the author's database. The database contains 280 original variants of the signature of one author and 1281 variants of counterfeit signatures of seven authors. To assess the statistical significance of differences in the accuracy and error rates of the fuzzy classifiers formed by metaheuristic algorithms, the Mann-Whitney (-Wilcoxon) U-test to compare medians and the Kruskal-Wallis test were used.

The presence of imbalance in data significantly complicates the classification task, including fuzzy systems. Due to a large number of instances of bigger classes, instances of smaller classes are not recognized correctly. Therefore, additional tools for improving the quality of classification are required. The most common methods for handling imbalanced data have several disadvantages. For example, methods for generating additional instances of minority classes can worsen classification if there is a strong overlap of instances from different classes. Methods that directly modify the fuzzy classification algorithm lead to a decline in the interpretability of the model. In this paper, we study the efficiency of the gravitational search algorithm in the tasks of selecting the features and tuning the term parameters for fuzzy classifiers of imbalanced data. We consider only data with two classes and apply the algorithm based on extreme values of classes to construct models with a minimum number of rules. In addition, we propose a new quality metric based on the sum of the overall accuracy and the geometric mean with the presence of a priority coefficient between them.