Currently, the solution of many problems of control, diagnosis, prognosis, there is the problem of describing the present uncertainty. This is due to the lack of information about the object under study. In this connection there is an objective need to formalize the description of uncertainty. The solution to this problem is important in the development of distributed intelligent information systems.
To describe the uncertainty traditionally used measure of entropy. The calculation of this index is based on estimates of the probabilities of the states of the object, which in the solution of practical problems is difficult to obtain.
An approach to formalizing the description of uncertainty in the information systems based on the theory of fuzzy sets. The uncertainty depends on the type of membership function. A case of complete uncertainty is described by a rectangular membership function.
The ratio of the area under the curve of a function belonging to a rectangular area of the membership function can be interpreted as a measure of uncertainty.
It should be noted that in a situation of complete uncertainty, probability theory and the theory of fuzzy sets are equivalent, as in any form can not allocate preferences regarding any values.
Thus, by using the theory of fuzzy sets mathematical description of uncertainty, which can be used in the development and management decisions.
Kofman A. Vvedenie
v teoriyu nechyotkix mnozhestv. Per. s francz. M.: Radio i svyaz'. 1982. 432 s.