Information Technology Reference
In-Depth Information
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
theories of Zadeh
Let us understand the term “a universal set” by Zadeh as “groups” and “groupings” or the
vocabulary of a language and sign it though - E. Then, the “elements of a set” by Zadeh and
“groups” by Piaget will be considered as the parts of speech. Let us sign these elements by x.
Search WWH ::

Custom Search