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Although there are many researches on statistical analysis for
fuzzy data, there are less discussions on possibility analysis
for fuzzy data. In this thesis, our goal is to construct a
possibility space for the analysis of fuzzy data. Especially we
propose the so-called double fuzzy variable. What is "
possibility "? Zadeh proposed the concept of fuzzy sets. Then
there are two types of description for the uncertainty : one
with randomness, the other with fuzziness. The former is dealt
with probability, and the latter with possibility. Although the
ideas of probability and possibility are different, the
constructions are similar. We will make a simple comparision of
these two in Chapter 2 and introduce the fuzzy variable which
is defined on possibility space. Then we propose the new idea "
double fuzzy variable " in Chapter 3 and also present its
properties. The combination of statistics and fuzzy data
produces fuzzy statistics; the combination of fuzzy theory and
fuzzy data produces the possibility analysis for fuzzy data. In
Chapter 3, we intepret the implicit features of double level
fuzziness and define the double fuzzy variable (d.f.v.). As a
result, double fuzzy variable becomes the means of handling
fuzzy data in possibility space. Furthermore, we define the
possibility distributions and fuzzy modal values of double
fuzzy variables. The topic in Chapter 4 is about parameter
estimation. Similar to the maximum likelihood principle in
statistics, we provide the maximum possibility likelihood
principle to estimate the unknown fuzzy parameter. Finally, we
take the normal possibility distribution as an example and
estimate its fuzzy parameters.
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