In this paper, we discuss the construction of fuzzy classifiers by dividing the task into the three following stages: the generation of a fuzzy rule base, the selection of relevant features, and the parameter optimization of membership functions for fuzzy rules. The structure of the fuzzy classifier is generated by forming the fuzzy rule base with
This article presents an approach for building fuzzy rule based classifi ers. A fuzzy rule-based classifi er consists of IF-THEN rules with fuzzy antecedents (IF-part) and the class marks in consequents (THEN-part). Antecedent parts of the rules break down the input feature space into a set of fuzzy areas, and consequents defi ne the classifi er exit, marking these areas with a class mark. Two main phases of building the classifi er are selected: generating the fuzzy rule base and optimizing the rule antecedent parameters. The classifi er structure was formed by an algorithm for generating the rule base by extreme features found in the training sample. The peculiarity of this algorithm is that it is generated according to one classifi cation rule for each class. The rule base formed by this algorithm has as low as practicable size in classifi cation of a given data set. The optimization of parameters of antecedents of the fuzzy rules is implemented using the monkey algorithm adapted for these purposes, which is based on observations of monkey migration in the highlands. In the process of the algorithm work, three operations are performed: climb process, watch jump process and somersault process. One of the algorithm's advantages in solution of high-dimension optimization problems is calculation of the pseudogradient of the objective function. Irrespective of the dimension at each iteration of the algorithm execution only two values of the objective function are to be calculated. The eff ectiveness of fuzzy rule-based classifi ers built with the use of the proposed algorithms was checked on actual data from the KEEL-dataset repository. A comparative analysis was conducted using the known analog algorithms "D-MOFARC" and "FARC-HD". The number of rules used by the classifi ers built with the use of the algorithms so developed is much lower than the number of rules in analog classifi ers with a comparable classifi cation accuracy, that points to the highest interpretability of the classifi ers built with the use of the proposed approach.
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.
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