Probabilistic mixtures provide flexible "universal'' approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs "naturally'' in one-pass mode. This is important in on-line applications and/or extensive databases. It even copes with dynamic nature of components forming the mixture. However, the quasi-Bayesian estimation relies on mixing via constant component weights. Thus, mixtures with dynamic components and dynamic transitions between them are not supported. The present paper fills this gap. For the sake of simplicity and to give a better insight into the task, the paper considers mixtures with known components. A general case with unknown components will be presented soon.
The paper addresses the problém of efficient and adequate representation of functions using two soft computing techniques: fuzzy logic and neural networks. The principle approach to the construction of approximating formulas is discussed. We suggest a generalized definition of the normál forms in predicate BL and ŁII logic and prove conditional equivalence between a formula and each of its normal forms. Some mutual relations between the normál forms will be also established.
The paper summarises basic properties of orthogonal polynomials and their use for approximation of functions representing a surface shape of optical components. The approximation of least-squares is demonstrated including its properties, and a strategy of a generation of orthogonal polynomials on a selected region is shown as well. The second part of the paper deals with mathematical description of aspherical optical surfaces. and Práce shrnuje základní vlastnosti ortogonálních polynomů a jejich využití pro aproximaci funkcí, které vyjadřují tvar ploch v rámci optické praxe. Aproximace funkce je představena ve smyslu nejmenších čtverců, jsou určeny její vlastnosti a možnost generace ortogonálních polynomů na libovolné oblasti. V druhé polovině práce jsou shrnuty možnosti matematického vyjádření asférických ploch v optice.
In the real-life engineering practice, non-linear regression models have to be designed rather often. To ensure their technical or physical feasibility, such models may, in addition, require another coupling condition. This paper describes two procedures for designing a specific non-linear model using AI methods. A Radial Basis Functions (RBF) based optimization is presented of the model using Genetic Algorithms (GA). The problem solved was based on practical measurements and experiments. The results presented in the paper can be applied to many technical problems in mechanical and civil engineering and other engineering fields. and Obsahuje seznam literatury
This paper is inspired by recent results [15, 16] which have shown that a multiplicative generator of a strict triangular norm can be reconstructed from the first partial derivatives of the triangular norm on the segment {0} x [0,1]. The strict triangular norms to which this method is applicable have been called zero-reconstructible triangular norms. This paper shows that every continuous triangular norm can be approximated (with an arbitrary precision) by a zero-reconstructible one, and thus substantiates the significance of this subclass of strict triangular norms.