313
Mari L, Savino M.,
Italian experience
837.
e. Cambridge Univ.
Hilary of basic and
nal Organization of
UNCERTAINTY IN MEASUREMENT: A SURVEY
Luca Mari
Libero Istituto Universitario C.Cattaneo
C.so Matteotti 22,21053 Castellanza (Va) - Italy
email: lmari@liuc.it
ISPRS Commission VI, Working Group 3
;sion of uncertainty
Organization of
"versky A., 1971.
emic Press, New
[1990).
3n and assignment
pp.79-90.
litative analysis of
ts, accepted for
f. Addison-Wesley,
»ychophysics, and
Ratoosh (eds.),
es, J.Wiley, New
KEY WORD: Foundations of Measurement, Measurement Uncertainty
ABSTRACT:
The paper analyzes the concept of non-exactness of measurement results, by clearly distinguishing between (i) the way
the results are expressed to make their uncertainty explicit; (ii) the way the chosen expression is interpreted as a suitable
combination of non-specificity and uncertainty; (iii) the way the interpreted results are formally dealt with. In this
perspective the merits and flaws of the ISO Guide to the expression of uncertainty in measurement are highlighted.
1. WHY NON-EXACTNESS IS AN ISSUE
IN MEASUREMENT
Measurement is a means to set a bridge between the
empirical world (to whom the measured thing belongs)
and the linguistic world (to whom the measurement result
belongs), aimed at enabling to faithfully re-interpret within
the empirical world the information that has been obtained
by handling symbols. The crucial point is the faithfulness
of such a re-interpretation. In terms of the following
diagram:
direct handling
“things” p “empirical results”
“symbols” — — ► “symbolic results”
processing
the issue is whether the procedures a and b would lead to
the same result.
The fact is that the two worlds are inherently different.
According to Bridgman, «there are certain human
activities which apparently have perfect sharpness. The
realm of mathematics and of logic is such a realm, par
excellence. Here we have yes-no sharpness. But this yes-
no sharpness is found only in the realm of things we say,
as distinguished from the realm of things we do. Nothing
that happens in the laboratory corresponds to the
statement that a given point is either on a given line or it is
not» (Bridgman, 1959).
The non-exactness (in the following the difference
between non-exactness and uncertainty will be
maintained and discussed) of measurement results
accounts for such a distinction, although «by forcing the
physical experience into the straight jacket of
mathematics, with its yes-no sharpness, one is discarding
an essential aspect of all physical experience and to that
extent renouncing the possibility of exactly reproducing
that experience. In this sense, the commitment of physics
to the use of mathematics itself constitutes, paradoxically,
a renunciation of the possibility of rigor» (Bridgman,
1959).
2. THE EXPRESSION OF NON-EXACT
MEASUREMENT RESULTS
Taking into account the linguistic side of the problem, the
first decision to be made is related to the form a
measurement result should be given to make its non
exactness explicit. According to the ISO Guide to the
expression of uncertainty in measurement (GUM) (ISO,
1993; a useful synthesis of the Guide can be found in
Taylor, Kuyatt, 1997):
meas. result =
=
where the first term of the couple could be obtained as the
average of the population of the instrument readings and
the second term as its estimated standard deviation.
Two notes in this regard:
* in presence of non-exactness the concepts of
measurement result and measurand value cannot dealt
with as equivalent: the measurement conveys information
not only on the measurand value, but also on its
uncertainty; in other terms, in this case a measurement
result is not complete without the indication of a degree of
uncertainty;
* different, and somehow more general, representations
could be chosen, for example subsets, or fuzzy subsets,
or probability distributions. All of these are more widely
applicable than the representation suggested by the
GUM, that can be employed only for algebraically strong
scales (although the generality is understood, because of
the applicability of the Chebyshev inequality, of
expressing measurement results as couples ,
