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6. Definition of Zadeh's fuzzy logic theory
Mathematical theory of fuzzy sets by Zadeh has allowed since more than a quarter of a
century ago up to now to describe fuzzy definitions and knowledge and operate with this
knowledge as well as make fuzzy outputs. (Пивкин , Бакулин и др)
The universal set is indicated by - E
Elements of a set are indicated by -- X
R - Indicates several properties, and x - indicates element E .
Ordinary (certain) Sub-set A of Universal Set E , whose elements
content the Property R, is indicated as the set of Ordered Pairs A = {m A ( х )/ х } , where m A ( х ) -
is a characteristic function, accepting
Value 1, if x contents Property R, and vice versa 0 .
Difference of a fuzzy sub-set from a certain one is that there is not a single valued answer
“yes-no” for the elements of x of E, regarding Property R .
In this respect, Fuzzy set A of Universal set E is indicated as the set of Ordered Pairs A =
{m A ( х of Sub-set A of Universal Set E .
7. Comparison of psychological theories by Piaget with mathematical