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Obtaining of ratings within the limits of quantitative characteristics [167] is
often enough reduced to determination of scalar integral indexes using vectors of
partial quantitative evaluations.
Methods of obtaining ratings within the limits of qualitative characteristics
[21—27. 168—170] use the approach [167] applied to qualitative characteristic
evaluation. However, this approach has some restrictions connected with peculi-
arities of scales used to measure qualitative characteristics, those restrictions are
considered in detail in § 1.2.
While estimating of qualitative characteristics verbal scales are used rather of-
ten, with numerical points, or elements of ordinal scales, put in correspondence to
levels of these scales. In the expert evaluation theory, the problem of determina-
tion of the numerical point collections put in correspondence to elements of ordi-
nal scales, is one of main problems [171]. In case of use of an unjustified arbitrary
collection of numerical points the stability of definitive conclusions is broken.
Thus, either the choice of a collection of the numerical points put in correspon-
dence to levels of verbal scales should be justified within the limits of each spe-
cific task, or a new approach (excluding necessity of operation with a particular
collection of numerical points) for determination of rating results should be
offered.
Methods [172—174] to obtain rating points of objects and groups of objects by
one and several qualitative and quantitative characteristics based on their linguistic
values are described below. These methods allow operating with abstract
values, namely, values of membership functions of linguistic values of estimated
characteristics rather than with numerical points.
Let us consider procedure of qualitative characteristic evaluation be simple, if
an expert refers an object to a certain verbal level of characteristic manifestation
and gives certain points corresponding to this level. For example, an expert esti-
mates convenience of software interface within the limits of a verbally-numerical
scale with four levels of a state: "inconvenient" — 1 point, "inconvenient enough"
— 2 points, "convenient enough" — 3 points, "convenient" — 4 points. Giving
certain points, the expert thereby defines a rating point for each object. However it
is necessary to note, that rather often such simple procedures of qualitative charac-
teristic evaluation give rough and approximate estimate which can be erroneous,
therefore these procedures need to be sophisticated.
Let us consider procedure of qualitative characteristic evaluation be complex, if
it consists of an evaluation of several sub-characteristics composing this character-
istic. An example of complex procedure of qualitative characteristic evaluation is
a procedure used to evaluate knowledge of students trained within the limits of a
certain subject by following components: academic achievements during a semes-
ter, testing results on different sections of the subject, participation in research
work within the limits of this subject etc. The result of a complex evaluation of
qualitative characteristic can be presented in the form of a vector with co-ordinates
being intermediate evaluations of the sub-characteristics. Then, a problem of ag-
gregation of separate evaluations into a uniform integral (rating) evaluation and
assignment of the accepted or specially developed gradation (verbal levels) to
objects within the limits of the characteristic considered.
