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Defuzzification
Centroid Defuzzification - Centre of gravity crisp representative
Defuzzification operator - centroid of area
Mamdani, E.H., Assilian, S.1975doi:10.1016/S0020-7373(75)80002-2 ↗
Overview
Centroid is the most widely used defuzzification method. It preserves the balance of the fuzzy set. Use for symmetric TFNs; for highly skewed FNs consider MOM or bisector.
- Output
- crisp score, higher is better
- Data
- Fuzzy (TFN), fuzzy numbers
- Size
- 1+ alternatives
- Used for
- Fuzzy MCDM, type-1 fuzzy systems
Fits when / Look elsewhere when
Fits when
- •Most widely used
- •Considers entire fuzzy set shape
- •Unique output
Look elsewhere when
- •Bimodal membership functions
Assumptions to verify
- Input is a valid fuzzy number (a ≤ b ≤ c or a ≤ b ≤ c ≤ d)
Limitations
- •Computationally expensive for general MFs (numerical integration)
Edge cases and pitfalls
Applying (a+b+c)/3 to trapezoidal FNs - wrong. Use the correct trapezoidal formula.
Dividing by 3 for symmetric FNs when the support is non-symmetric - always check.
Works with
How to cite
Mamdani, E.H.; Assilian, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies. https://doi.org/10.1016/S0020-7373(75)80002-2
System ID, as it appears in reports and the API
DEFUZZ-CENTROID