Information Technology Reference
In-Depth Information
homogeneous events, the valence probability is a statistical (classical) one. The
axiological probability expresses expectancy of hypothesis realization taking into
account a context of value judgments advanced by one or several experts
regarding an object of research. When using such probability, risk of arbitrariness
and erroneous prognosis of object behavior increases invariably. Besides, analyses
of expert evaluations showed that thoughts and judgments of experts are
non-additive, which means that measures used by experts are free from additivity
property which is inherent to a probability measure.
Attempts to formalize expert logical-linguistic expressions and value judgments
of observable properties of a certain object resulted in led emergence of the fuzzy
set theory developed by L. Zadeh. In 1965 in the “Information and Control”
journal he published his “Fuzzy Sets” paper [14] which became a powerful
impetus for theoretical evidences and applied researches in various areas with
active participation of human experts.
L. Zadeh relied on a premise saying that outcome of human thinking is not a set
of numbers, but elements of some fuzzy sets or classes of objects, for which
transition from "membership" to “non-membership” is not intermittent, but
continuous. He understood that use of such objects is a means to improve stability
of mathematical models of real human activity events.
Distinction between fuzziness and randomness leads to the fact that methods of
the fuzzy set theory are not similar to probability theory methods, they are simpler
in many aspects, because they are based on the simpler concept of membership
function (by L. Zadeh) in comparison with a probability distribution function
which assumes definition of a probability measure generating this function [15].
Obviously, the information obtained from experts can contain both accurate and
fuzzy data. Fuzzy data arise from use of linguistic values of estimated
characteristics within the scope of professional language of experts. The
information containing fuzzy data was called the fuzzy expert information.
The history of the fuzzy set theory can give some examples of the unsuccessful
practical applications caused by badly considered adherence to the new scientific
direction. That is why it is necessary to define a class of problems for which its
use is expedient. This class is characterized with complexity of quantitative
evaluation of objects and processes considered, presence of information difficult
to formalize accompanied with uncertainty of nonrandom nature, necessity of
accounting for individual characteristics and peculiarities of persons (experts) in
charge of making evaluations.
1.2 Scales and Admissible Transformations
Let us consider known scales and admissible transformations of characteristic
values measured within these scales. It is known that a transformation which
keeps substantial sense of the given aspect of measurement [16] is called an
admissible transformation of the measured characteristic values. To measure
quantitative characteristics the following scales are used, in particular, absolute,
ratio, interval, difference.
