Information Technology Reference
In-Depth Information
Verbal scales are used often enough to describe physical values of quantitative
characteristics. For example, in [35. 36], to describe a “steam pressure at inlet”
(with a range [1.1; 6.7]) parameter of a high pressure preheater intended to
improve turbine plant efficiency, the verbal scale with levels “low pressure”,
“pressure close to 4”, 'high pressure” is used. Another example is the verbal scale
used to describe event probabilities. As known, an event probability is usually
expressed by numerical value and varies from 0 to 1. However, for example, when
speaking about the probability of an enterprise bankruptcy, the manager of this
enterprise is interested not in a precise figure, which is likely to be little-
informative for him, but in definition of one of verbal levels of bankruptcy
probability, in particular, "very low", "low", "mean", "high", "very high" [37].
With a range of definition (universal set) of quantitative characteristic and
levels of a verbal scale known, an expert divides this area into non-overlapping
sets which correspond to verbal levels. However, such approach is featuring with
essential shortage which lies in the fact that while describing objects with
boundary values of an indicator, an expert experiences difficulties caused by
intermittent transitions between values.
This shortage can be remedied with the fuzzy set theory in which not precise
intervals of values are put in correspondence to verbal levels of quantitative
property, but fuzzy sets. The resultant verbal-fuzzy scale is referred to as a
linguistic scale [38—39]. As a result of such buildings, a quantitative
characteristic, on the one hand, is corresponded with physical values measured by
a technical instrument and, on the other hand, with linguistic values "measured"
by an expert. Each physical value belongs to some linguistic one with certain
degree of expert confidence.
Building of a linguistic scale for qualitative characteristics is much more
complicated. If a verbal-numerical scale for qualitative characteristics represents a
collection of verbal levels with the corresponded collection of numbers (elements
of an ordinal scale), then a linguistic scale is a collection of verbal levels with a
collection of the corresponded fuzzy sets specified at some universe. As
qualitative characteristics cannot be measured objectively (by instrument), the
universal sets applicable for them cannot be unambiguously defined, as they do
for quantitative characteristics. Definition of universal set is made within the
scope of each qualitative characteristic and requirements of each specific task.
Thus, expedient values of linguistic scales for qualitative characteristics are fuzzy
sets. In the mathematical statistics, collections of numerical data and corresponded
chance quantities are referred to as sampling; similarly, in the fuzzy set theory verbal
levels and corresponded fuzzy sets are referred to as linguistic values.
Definition of linguistic values of characteristics (based on the fuzzy set theory)
makes it possible to operate not with values of the characteristics which are non-
comparable among themselves by substance and content (as they are estimated in
different scales and having different dimensions), but with dimensionless values
of membership functions.
