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Hiroshi Watanabe
COARSE-GRAINED INFORMATION AND ITS APPLICATION TO A FORMAL THEORY OF MEASUREMENT

Measurement is an acquisition of the knowledge of the external world, and there is little doubt that our concept and scientific theories depend strongly on the relations such as correlation and probabilistic dependences we discover in a number of observed data. However, measurement is not determined only by the measured object but depends on various factors, one of which is the degree of the fineness of observation. The present paper is an effort to introduce this subject into a formal framework of measurement science. Taking advantage of entropic measure of interdependence, we examine the nature of information obtained by coarse nominal measurement, where some symbols are put into one group as the same symbol, regarding it as a kind of clustering task, and propose a possible formal approach to group formation procedure as coarse observation of objects. Information-theoretical interdependence is often measured by entropy function. However, in grouping of objects, our result suggests that we should take rather the average entropy as the measure of the degree of interdependence.

Valery Granovsky
MEASUREMENT THEORY: VIEW FROM METROLOGICAL PRACTICE

Measurement theory is developed as partial theory of uniform quantities group measurement and as general measurement theory. In contrast to this, the applied metrology has to ensure the quality of practical measurements supporting industrial, technical, or research activity. The mission of the measurement theory is to serve as a base for applied metrological methods and procedures. But actually the measurement theory pays just a little attention to the practical problems, and affects weakly and indirectly the applied metrology. General measurement theory has the abstract measurement equation as its object and studies special kinds of the equation. Partial measurement theory addresses to metrological measurements, which serve for unit transportation from reference standard to measuring instrument. This transportation goes on during normal conditions. Applied metrology problems are connected with that it is impossible to realize the unit with the necessary accuracy in any unique measurement act because of affecting object peculiarities and/or measurement conditions. So, there are two general methodical problems arising in practice: (i) to realise unit in the conditions different from the normal ones, and (ii) to compare the unit with the inherent characteristic of real object, which is quite different from the abstract general model of the physical quantity. So the approach to uniformity of measurements, which is alternative to the traditional one, is to use “reference object” and to certificate it metrologically under the working conditions.

Karl H. Ruhm
SCIENCE AND TECHNOLOGY OF MEASUREMENT – A UNIFYING GRAPHIC-BASED APPROACH

Graphic-based representations of theoretical ideas are always useful bases of discussions. This is especially true for measurement sciences where structures are of utmost complexity. It will be shown that these structures are mainly structures of Signal and System Theory.

Graçaliz P. Dimuro, Antônio Carlos R. Costa, Vladik Kreinovich
MODELLING MEASUREMENTS AS TIMED INFORMATION PROCESSES IN SIMPLEX DOMAINS

This paper presents a domain-theoretic model for measurements and measuring instruments, by making explicit in simplex-domain structures two important aspects of measurement processes: the notion of standard representation relation, established between the (physical) values that are being measured and the meanings of the readings (semantic values) of the measuring instruments used to measure them, and the time underlying every meas-urement process, in a way that it is possible to trace the history of every measuring process. We also present the modelling of measurements performed by combined meas-uring instruments synchronized in time. Finally, the domain-theoretic modelling of a sample measuring process is pre-sented to illustrate the approach.

Hung T. Nguyen, Vladik Kreinovich, Chitta Baral, Valery D. Mazin
GROUP-THEORETIC APPROACH AS A GENERAL FRAMEWORK FOR SENSORS, NEURAL NETWORKS, FUZZY CONTROL, AND GENETIC BOOLEAN NETWORKS

When describing a system of interacting genes, a useful approximation is provided by a Boolean network model, in which each gene is either switched on or off – i.e., its state is described by a Boolean variable.
Recent papers by I. Shmulevich et al. show that although in principle, arbitrarily complex Boolean functions are possible, in reality, the corresponding Boolean networks can be well described by Boolean functions from one of the socalled Post classes – classes that are closed under composition. These classes were originally described by E. Post.
It is known that the Boolean model is only an approximate description of the real-life gene interaction. In reality, the interaction may be more complex. How can we extend these results to more realistic continuous models of gene interaction?
In this paper, we show that the Post class approach can be viewed as a particular case of a general group-theoretic framework that has already led to a successful justification of empirical formulas from such areas of signal processing as sensor analysis, neural networks, fuzzy techniques, etc. Because of this relation, we suggest group-theoretic approach as a framework for describing gene interaction in a more realistic way.

R. Osegueda, G. R. Keller, S. A. Starks, R. Araiza, D. Bizyaev, V. Kreinovich
TOWARDS A GENERAL METROLOGY FOR DESIGNING SUB-NOISE MEASUREMENT PROCEDURES

In many practical situations, the measurement result z depends not only on the measured value x, but also on the parameters s describing the experiment’s setting and on the values of some auxiliary quantities y; the dependence z = f(x; s; y) of z on x, s, and y is usually known. In the ideal case when we know the exact value of the auxiliary parameter y, we can solve the above equation and find the desired value x. In many real-life situations, we only know y with some uncertainty, and this uncertainty leads to additional uncertainty in x.
If we are trying to reconstruct x based on a single measurement result, then, of course, the measurement error in y leads to the corresponding measurement error in x – and, unless we perform more accurate measurements, we cannot improve x’s accuracy.
In many practical situations, however, if we have several measurement results corresponding to different values of t and/or y, we can reconstruct x with a much higher accuracy – because we can combine these measurement results in such a way that the influence of y drastically decreases. As a result, we get a sub-noise measurement accuracy, the accuracy that is much better than the accuracy with which we know y.

Luca Mari
ON THE “PARADOX OF FOUNDATION” FOR MEASUREMENT

Given the common assumption that measurement plays an important role in the foundation of science, the paper analyzes the possibility that measurement science, and therefore measurement itself, can be properly founded. The conclusion, that such a position unavoidably leads to paradoxical situations, opens the discussion for a new epistemology of measurement, whose characteristics and interpretation are still to be investigated.

Dietrich Hofmann, Gerhard Linss
INFLUENCE OF INTERNET METROLOGY ON ADVANCES OF MEASUREMENT SCIENCE

Aim of the paper is to present different definitions of measurement, to prove, that measurement science is metroloy, to illustrate the advantages of Internet-metrology to show the influence of standpoints on definitions, to define measurement paradigms for practical use.

Peter Sydenham, Richard Thorn
DEVELOPING A MEASURING SYSTEMS BODY OF KNOWLEDGE

This paper discusses issues to be considered in setting up a Measuring System Body of Knowledge, an MSBOK. It covers the benefits of it being available; what it should contain; why online delivery is required; and progress being made on a project developing such a knowledge service for those who need reliable and rapid access to measurement knowledge.

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