Concept
Logic of degrees between true and false — for rice cookers, washing machines, and AI.
Understand it in one breath
A fuzzy set assigns each object a degree of membership between 0 and 1, such as how strongly a day belongs to the set “warm.” Fuzzy logic extends this idea to degrees of truth and logical operations, making vague boundaries computable. Depending on context, 0.7 is a membership or truth degree rather than a probability; control systems use such values to connect sensor readings with gradual rules.
At a glance
"It is warm today" | Classical logic | Fuzzy logic |
|---|---|---|
10°C | False (0) | 0.1 (hardly warm) |
18°C | False (0) | 0.5 (borderline) |
22°C | True (1) | 0.7 (warm) |
28°C | True (1) | 0.95 (quite warm) |
35°C | True (1) | 0.4 (hot — membership falls again) |
The membership function μ_A(x) gradually approaches 1, peaks, then falls again — a mathematical model of the natural flexibility of human language.
Key formula
Key moments
Zadeh — the paper Fuzzy Sets
Lotfi Zadeh proposed sets whose elements can have partial degrees of membership. The idea initially attracted little attention.
Japan’s fuzzy-appliance boom
Japanese manufacturers introduced rice cookers, washing machines, and other appliances using fuzzy control, helping make the approach a consumer-technology phenomenon.
The Sendai subway
An automated subway system using fuzzy control delivered smoother acceleration and braking, becoming a celebrated real-world demonstration of the technology.
Modern applications
Fuzzy control in rice cookers, washing machines, and air conditioners; ABS braking; camera autofocus; degrees of diagnostic confidence; and partial conclusions in AI.
Beyond MathVoyage
Loading…