Definition:Fuzzy Set Theory

Definition

Fuzzy set theory is a version of set theory in which the membership relation is not precisely defined.

Hence the membership relation is represented by a real number between $0$ and $1$:

$0$ meaning definitely not an element

$1$ meaning definitely an element.

Examples

Tallness

Whether a person is tall or not is not a question which can be answered with an absolute true or false.

Whether or not you are tall is a matter of degree.

Hence the property of tallness can be modelled using a fuzzy set.

Also see

• Definition:Fuzzy Logic

• Results about fuzzy set theory can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): fuzzy set theory
• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: Footnote $^3$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): fuzzy logic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fuzzy logic