THEORY OF COARSE-GRAINED INFORMATION

Hiroshi Watanabe

Abstract

Measurement should be objective in principle. However, the accuracy of measurement often depends on various factors, including instruments of measurement, adopted intentionally or made available accidentally, and from a practical point of view, it is important to choose a suitable degree of the accuracy of measurement for the intention of measurement. The present paper discusses some information-theoretical aspects of the relationship between the degree of the accuracy of nominal description of objects and the interdependence among groups of those objects within a formal framework of clustering, where a new entropic measure of interdependence is applied to estimate the change of the interdependence when the nominal description becomes more `coarse’ so that several objects appear to be identical, and are grouped into the same class. The degree of interdependence is often measured by (sum of entropies of partial systems) - (entropy of the whole). Close examination shows, however, that instead of simple formal entropy we should take rather (the number of the members of a group) × (entropy of the group). The result also implies that in integration of information channels the average entropy plays an important role. A brief discussion is also made on elicitation of so-called information granules.

Keywords

clustering, elicitation of information granule, interdependence analysis, measurement science, minimum average entropy

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PWC-2003-TC7-027.pdf

DOI

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IMEKO TC

TC7 - Measurement Science

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