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Defuzzification
Gaussian Centroid Defuzzification - Crisp representative of Gaussian fuzzy number
Defuzzification operator - Gaussian membership function
Zadeh, L.A.1965doi:10.1016/S0019-9958(65)90241-X ↗
Overview
For symmetric Gaussian: defuzzified value = μ directly (no computation needed). σ only matters for overlap and aggregation, not defuzzification. For asymmetric Gaussian: x* shifts toward the heavier tail.
- Output
- crisp score, higher is better
- Data
- Gaussian Fuzzy, gaussian fuzzy numbers
- Size
- 1+ alternatives
- Used for
- Fuzzy MCDM, engineering fuzzy systems
Fits when / Look elsewhere when
Fits when
- •Trivial for symmetric case: x*=μ
- •Closed-form for asymmetric two-sided Gaussian
Look elsewhere when
- •TFN/trapezoidal inputs - use DEFUZZ-CENTROID
Assumptions to verify
- σ > 0
- Symmetric Gaussian assumed unless σ_L, σ_R specified separately
Limitations
- •Gaussian FNs less common in MCDM literature than TFN
- •σ carries no ranking information after defuzzification
Edge cases and pitfalls
Confusing σ with support width - σ does not affect centroid for symmetric Gaussian.
Applying TFN formula (a+b+c)/3 to Gaussian FNs - wrong type, use x*=μ.
Works with
How to cite
Zadeh, L.A. (1965). Fuzzy sets. Information and Control. https://doi.org/10.1016/S0019-9958(65)90241-X
System ID, as it appears in reports and the API
DEFUZZ-CENTROID-GAUSSIAN