Over the last several decades, neuro-fuzzy systems (NFS) have been widely analyzed and described in the literature because of their many advantages. They can model the uncertainty characteristic of human reasoning and the possibility of a universal approximation. These properties allow, for example, for the implementation of nonlinear control and modeling systems of better quality than would be possible with the use of classical methods. However, according to the authors, the number of NFS applications deployed so far is not large enough. This is because the implementation of NFS on typical digital platforms, such as, for example, microcontrollers, has not led to sufficiently high performance. On the other hand, the world literature describes many cases of NFS hardware implementation in programmable gate arrays (FPGAs) offering sufficiently high performance. Unfortunately, the complexity and cost of such systems were so high that the solutions were not very successful. This paper proposes a method of the hardware implementation of MRBF-TS systems. Such systems are created by modifying a subclass of Takagi-Sugeno (TS) fuzzy-neural structures, i.e. the NFS group functionally equivalent to networks with radial basis functions (RBF). The structure of the MRBF-TS is designed to be well suited to the implementation on an FPGA. Thanks to this, it is possible to obtain both very high computing efficiency and high accuracy with relatively low consumption of hardware resources. This paper describes both, the method of implementing MRBFTS type structures on the FPGA and the method of designing such structures based on the population algorithm. The described solution allows for the implementation of control or modeling systems, the implementation of which was impossible so far due to technical or economic reasons.

The pension system’s construction is an important element of the public finance system and the state budget policy. It is a relevant and important topic from the perspective of the level of cash benefits for future retirees after they finish their professional careers.The aim of the paper is to present and analyze the evolution of solutions in the construction of the pension system in Poland since its first reform in 1999. The paper analyzes various options of investing for future pensions allowed by law in Poland. Simulations of the levels of future pension benefits are based on different variations, including membership or non-membership in an Employee Capital Plan and membership or non-membership in an Individual Retirement Account after the liquidation of Open Pension Funds.According to the calculations, the future pensioner can count on the total payment from the commercial pillars, assuming the average life expectancy in Poland is reached: PLN 230,100 (Option I), PLN 346,698 (Option II), PLN 187,643 (Option III), and PLN 304,240 (Option IV), respectively.It is an emphasized fact that ensuring the living standard’s expected level after reaching retirement age is strictly dependent on voluntary investments for future benefits during professional activity.

The aim of the article is to investigate the impact of algorithmic trading on the returns obtained in the context of market efficiency theory. The research hypothesis is that algorithmic trading can contribute to a better rate of return than when using passive investment strategies. Technological progress can be observed in many different aspects of our lives, including investing in capital markets where we can see changes resulting from the spread of new technologies. The methodology used in this paper consists in confronting a sample trading system based on classical technical analysis tools with a control strategy consisting in buying securities at the beginning of the test period and holding them until the end of this period. The results obtained confirm the validity of the theory of information efficiency of the capital market, as the active investment strategy based on algorithmic trading did not yield better results than the control strategy.

In the verification of identity, the aim is to increase effectiveness and reduce involvement of verified users. A good compromise between these issues is ensured by dynamic signature verification. The dynamic signature is represented by signals describing the position of the stylus in time. They can be used to determine the velocity or acceleration signal. Values of these signals can be analyzed, interpreted, selected, and compared. In this paper, we propose an approach that: (a) uses an evolutionary algorithm to create signature partitions in the time and velocity domains; (b) selects the most characteristic partitions in terms of matching with reference signatures; and (c) works individually for each user, eliminating the need of using skilled forgeries. The proposed approach was tested using Biosecure DS2 database which is a part of the DeepSignDB, a database with genuine dynamic signatures. Our simulations confirmed the correctness of the adopted assumptions.