Fuzzy Logic

Fuzzy logic is a form of logic that deals with approximate reasoning rather than fixed and exact values. Unlike classical logic, where variables are either true $(1)$ or false $(0),$ fuzzy logic allows variables to have values between $0$ and $1,$ representing degrees of truth.

Differences from Classical Logic

Truth Values:

Classical Logic: Variables are true $(1)$ or false $(0).$

Fuzzy Logic: Variables range between $0$ and $1.$

Handling Uncertainty:

Classical Logic: Uses precise, binary decisions.

Fuzzy Logic: Manages uncertainty and imprecision.

Rule Application:

Classical Logic: Uses strict rules.

Fuzzy Logic: Uses flexible, partial truth rules.

Real$-$World Scenario: Temperature Control

Scenario:

Designing a smart thermostat to maintain a comfortable temperature.

Classical Logic:

Below $18\backslash$deg C: Turn heater on$.$

Above $22\backslash$deg C: Turn heater off.

Fuzzy Logic:

Variables: Temperature $($Cold$,$ Cool, Warm, Hot$)$ and Heater output $($Low$,$ Medium, High$).$

Rules: If temperature is Cold, set heater to High; if Cool, set to Medium; if Warm, set to Low; if Hot, turn off.

Example:

At $20\backslash$deg C$,$ fuzzy logic might consider it $70\%$ Cool and $30\%$ Warm, setting the heater to a blend of Medium and Low for efficient comfort control.

Conclusion

Fuzzy logic allows for partial truths and better handles real$-$world complexity, making it more effective for systems like temperature control compared to classical logic$\text{'}$s strict binary rules.