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Highlights: [•] We propose a new dynamic signature verification system using vertical partitioning. [•] In our algorithm partitions represent moments of signing process. [•] Our algorithm takes advantage of fuzzy sets and systems theory. [•] Our algorithm allows to extract knowledge about the signature verification. [•] Our algorithm takes into account hierarchy of partitions individually for each user. [Copyright &y& Elsevier]

In this work, we consider the flexible neuro-fuzzy systems of the Mamdani-type. When designing such systems to solve approximation problem, we should choose triangular norms used in inference and aggregation operators. This can be done by trial and error. In this work, we propose an algorithm that allows in an automatic way to choose the types of triangular norms in the learning process. The task of this algorithm is also an automatic selection of parameters of all functions describing the system. The algorithm uses an evolutionary strategy for its action and has been tested using well-known approximation benchmarks. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of neuro-fuzzy systems. Moreover, we develop a novel method for reduction of such systems without the deterioration of their accuracy. The reduction algorithm gradually eliminates inputs, rules, antecedents, and the number of discretization points of integrals in the center of area defuzzification method. It then automatically detects and merges similar input and output fuzzy sets. Through computer simulations it is shown that accuracy of the system after reduction and merging has not deteriorated despite the fact that in some cases up to 54% of various parameters and 74% of inputs were eliminated. The reduction algorithm has been tested using well-known classification benchmarks. [ABSTRACT FROM AUTHOR]

Abstract: In the paper, the evolutionary strategy is applied for learning flexible neuro-fuzzy systems. In the process of evolution we determine: fuzzy inference (Mamdani type or logical type—described by an -implication), specific fuzzy implication, if the logical type system is found in the process of evolution or specific -norm connecting antecedents and consequences, if the Mamdani type system is found in the process of evolution, specific -norm for aggregation of antecedents in each rule, specific triangular norm describing aggregation operator, shapes and parameters of fuzzy membership functions, weights describing importance of antecedents of rules, and weights describing importance of rules, parameters of adjustable triangular norms, parameters of soft triangular norms. It should be noted that the crossover and mutation operators are chosen in a self-adaptive way. The method is tested using well known classification benchmarks. [Copyright &y& Elsevier]