Information Technology Reference
In-Depth Information
Chapter 1
The Basic Concepts of the Fuzzy Set Theory
1.1 Uncertainty Classification
The common feature of problems solvable with active participation of experts is
presence of the versatile information which is difficult for mathematical
formalization within the scope of traditional concepts. It is partly connected with
the fact that while describing or estimating real objects and situations experts use
words of a natural language to reflect their subjective experience, judgment, sights
and interests. Use of such words brings uncertainty to information obtained from
an expert in the form of fuzziness. In usual languages the concepts of uncertainty,
fuzziness and randomness tend to mix up, however they were differentiated in a
language of science many years ago. With this assumption, to review such
philosophical concept as uncertainty, the following classification [1] illustrated by
Fig. 1.1 is recommended to use.
Uncertainty of object
description
Physical Linguistic
Inaccuracy Randomness word meaning sense of phrases
Homonymy Fuzziness of content
Theory of Probability Theory of
Measuring Theory formal
grammar
Formal Scaling
language theory
theory Theory of
fuzzy sets
Fig. 1.1
Classification of object description uncertainties
