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Set theory · Concept hubDeep story

Fuzzy Logic

1965 CE20th-century United States (Zadeh)

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

μA:X[0,1]\mu_A: X \to [0,1]

Key moments

1965 CE

Zadeh — the paper Fuzzy Sets

Lotfi Zadeh proposed sets whose elements can have partial degrees of membership. The idea initially attracted little attention.

1985 CE

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.

1990 CE

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

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