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Every expert, while compiling «his» classification independently of
ether experts, derives a classification M ’ from the multitude {M} with a
probability P(M’). In case when the probability P(M’) is given by the ex­
pert as a degree of an authenticity of his classification M ’ we are getting
the appraisal of the type (2.9).

      Appraisals of the type (2.10).
      As an example of the appraisals of the type (2.10) it is possible to con­
sider the appraisals in which the expert defines an entire group of events
(A1?Ag, ..., An) and the vector of probabilities p = (pp p2, ....pn) while indi­
cating for every A a probability p; = p(A) in such a way that the sum ХГ P
= 1. Such appraisals may be considered as the p —mixtures [63].
      Appraisals of the type (3.7).
      The appraisals of this type are discussed, for example, by B.G.
Mirkin. In this case the expert is supposed to appraise an intensity of his
preference in figures for every pair of objects [58].
      Appraisals of the type (3.9).
      In the case when an expert makes a pair comparison > \ and a
probability p (Xt > X2) of the fact that the object At is more preferable
than the object A2where X,, X2are the values of the objects A, and A2in
the psychological continuum of the expert we are obtaining the apprais­
als of the type (3.9).
      The statistical models of the pair comparisons are discussed in nu­
merous works beginning from the work of Terstone [184]. The work of
Yu.N. Tyurin, A.P. Vasiljevich, P.P. Androukovich [94] is an example of
experimental research works in this direction.
      Appraisals of the type (4.9).
      By analogy with the appraisal of the type (3.9) the experts suggest
an appraisal obtained with the multiple comparisons method, and in addi­
tion they give an estimation of a probability as a confidence degree of their
appraisal. The appraisals of this type are described in the review [108].
      Appraisals of the type (5.9).
      As well as the appraisals of the type (3.9) and (4.9) the —appraisals
of the type (5.9) are obtained in that case when an expert gives a ranging
and an estimation of a probability as a degree of a certitude in his ap­
praisal. A review of statistical models of the ranging is discussed in the
works of D.S. Shmerlingand others [108].

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