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SUFFICIENCY AND FUZZINESS IN RANDOM EXPERIMENTS

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MARÍA ANGELES GIL

*Departamento de Matemáticas, Universidad de Oviedo,*

C/Calvo Sotelo, s/n, 33007 Oviedo, Spain
(Received April 2, 1990; revised November 19, 1990)

**Abstract.**
In previous papers, the consequences of the ``presence of
fuzziness'' in the experimental information on which statistical inferences are
based were discussed. Thus, the intuitive assertion «fuzziness
entails a loss of information» was formalized, by comparing the
information in the ``exact case'' with that in the ``fuzzy case''. This
comparison
was carried out through different criteria to compare experiments (in
particular,
that based on the ``pattern'' one, Blackwell's sufficiency criterion). Our
purpose
now is slightly different, in the sense that we try to compare two ``fuzzy
cases''.
More precisely, the question we are interested in is the following: how will
different ``degrees of fuzziness'' in the experimental information affect the
sufficiency? In this paper, a study of this question is carried out by
constructing
an alternative criterion (equivalent to sufficiency under comparability
conditions),
but whose interpretation is more intuitive in the fuzzy case. The study is first
developed for Bernoulli experiments, and the coherence with the axiomatic
requirements for measures of fuzziness is also analyzed in such a
situation. Then it
is generalized to other random experiments and a simple example is examined.

*Key words and phrases*:
Blackwell's sufficiency, fuzziness, fuzzy
information, random experiment, probability of a fuzzy event.

**Source**
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