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

Hiroshi Watanabe

Abstract

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.

Keywords

measurement science, nominal scale, entropic measure of interdependence

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IMEKO-TC7-2004-113.pdf

DOI

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IMEKO TC

TC7 - Measurement Science

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