Project:DMEU/Интуиционистки размити множества

Изследване на възможностите за използване на Data Mining за управление на процеси в електронен университет За проекта За тематиката Data mining Обобщени мрежи Интуиционистки размити множества Колектив Цели и задачи Научни резултати Научни форуми Data Mining in Electronic University (DMEU)

Интуиционистки размитите множества (Intuitionistic fuzzy sets) са множества, чиито елементи имат степени на принадлежност и непринадлежност. Те са дефинирани от Красимир Атанасов (1983) като разширение на размитите множества на Lotfi Zadeh.

In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition — an element either belongs or does not belong to the set.
As an extension, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0, 1].
The theory of intuitionistic fuzzy sets further extends both concepts by allowing the assessment of the elements by two functions: for membership and for non-membership, which belong to the real unit interval [0, 1] and whose sum belongs to the same interval, as well.

Intuitionistic fuzzy sets generalize fuzzy sets, since the indicator functions of fuzzy sets are special cases of the membership and non-membership functions and of intuitionistic fuzzy sets, in the case when the strict equality exists: , i.e. the non-membership function fully complements the membership function to 1, not leaving room for any uncertainty.