Michał K. Urbański

Fuzzy approach to the theory of measurement inexactness

Abstract In this paper we propose the t -norm based arithmetics to describe the propagation of both systematic and statistical inexactness. Evaluation of measurement inexactness occurs in three steps: (1) estimation of inexactness of single ‘pure’ measurement results, (2) propagation of inexactness due to statistical evaluation, (3) estimation of measure of inexactness. In our proposition results of single measurements are fuzzy intervals, propagation of inexactness are described by fuzzy arithmetic based on t -norm. The measure of inexactness is half width of α -cut (instead of confidence interval in statistical approach). Arithmetic operators are obtained by applying the generalization of Zadeh’s extension principle based on t -norm. The averaging operator defined in the framework of t -norm arithmetics decreases the statistical component and does not change the systematic component of inexactness.

Fuzzy arithmetic based on boundary weak t-norms

In this paper we propose the new extended class of t-norm operators called the boundary weak. The aim of the extension of this operator is that the sum of the fuzzy numbers in the arithmetic based on such t-norm gives the more narrow fuzzy number if compared to arithmetic based on standard t-norm. This extension is based on the replacement of the condition T(x, 1) = x by the weaker one: T(x, 1) ≤ x, for x ∈ [0,1].

On the improvement of the metrological properties of manganin sensors

The paper presents the recent progress made in the accuracy improvement of the manganin pressure sensors at the Warsaw University of Technology (WUT) and at the Institute of Nuclear Energy. The efforts of the authors were concentrated on three problems: The improvement of the temperature characteristics by the design of a manganin sensor with the temperature compensation achieved by the application of two manganin coils with two different temperature characteristics; The improvement of the calibration process by using a high pressure deadweight piston gauge (with the correction of effective area versus pressure dependence, built at WUT), measurements of the manganin resistance as a function of the temperature and of the pressure using a precise multimeter and application of statistical methods for long series of measurements. The modification of the thermal characteristic by implantation of bismuth and krypton ions.

A note on Nguyen--Fullér--Keresztfalvi theorem and Zadeh's extension principle

This paper is devoted to the analysis of the generalised form of the Nguyen-Fuller-Keresztfalvi theorem (NFK theorem). The classical NFK theorem expresses the Zadeh extension principle in terms of @a-cuts of fuzzy sets, but it is subjected to some constraining assumptions. These assumptions concern all data in the problem: shape of fuzzy sets, topology of underlying spaces, and regularity of functions and t-norms. In this paper we analyse consequences of dropping these assumptions. In order to prove the generalised version of the NFK theorem, we introduce a notion of level sets as a generalisation of the collection of @a-cuts. We discuss properties of the level sets and then we formulate the general NFK theorem, which does not require assumptions on the shape of fuzzy sets, t-norms, nor topology of underlying spaces. Finally, we return to the classical formulation of the NFK theorem and we show that it can be extended to the class of fuzzy sets with unbounded supports.

On the field nature of measuring process

Abstract Basing upon the philosophical assumption that it is not possible to develop a theory of measurement independent from the physical nature of the measured object, we formulate the topological theory of measurement. The model of measurement is a fibre bundle space with the base space D representing topological properties of measured quantity (measurement quantity base space) and fibres F corresponding to the algebraic properties of space values of measured quantity (properties of scale). We introduce a join operation ∗ of two base spaces defining base space of measurement of two quantities ( D=D 1 ∗D 2 ) . This topological model of measurement is consistent with the field theory.

The theory of amorphous silicon in the coherent potential approximation (CPA)

The single-site CPA self-consistent condition for the effective non-diagonal disorder Hamiltonian of amorphous silicon is obtained. Simplified tightbinding model Hamiltonian of the s-and p-bands is assumed. Partial and total density of electronic states numerical calculation of amorphous silicon is presented.

Stepped piston modification in the piston manometer of mixed operational principle (simple-piston and re-entrant cylinder system)

The optimization of mixed-principle operation pressure balance consisting of two parts: simple-piston and re-entrant cylinder units is reported. The maximum high pressure corrections for low pressure effective area of the system can be reduced by 50%. The solution was obtained by application of a small reduction (step) of the piston diameter. The modified design is characterized by the performance of the metrological piston of 10 mm2 nominal cross-sectional area with a (1–3) μm inward circumferential step located between the upper (simple piston) and lower (re-entrant) parts of the cylinder in the area where existing intermediate pressure is constant.

The resistance pressure gauge with a linear unbalanced DC bridge and correction of nonlinear sensor characteristics

Abstract The circuit of an unbalanced DC bridge in which its output voltage signal is proportional to the increase of resistance and a simple manner of correction of the nonlinear characteristics of the sensor are described. The high pressure cell up to 1 GPa is also briefly described.