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Defuzzification
Bisector of Area Defuzzification - Vertical line dividing fuzzy set area equally
Defuzzification operator - bisector of area
van Leekwijck, W., Kerre, E.E.1999doi:10.1016/S0165-0114(97)00337-0 ↗
Overview
Bisector = 'median' of fuzzy set. For symmetric TFNs: bisector = centroid = mode. For asymmetric: bisector is between centroid and the lighter tail. Use alongside centroid to assess sensitivity to defuzzification method.
- Output
- crisp score, higher is better
- Data
- Fuzzy (TFN), fuzzy numbers
- Size
- 1+ alternatives
- Used for
- Fuzzy MCDM
Fits when / Look elsewhere when
Fits when
- •Robust to outliers in MF shape
- •Unique output
- •Median interpretation
Look elsewhere when
- •Symmetric TFNs (use centroid/MOM - same result, simpler)
Assumptions to verify
- Input is a valid TFN or trapezoidal FN
Limitations
- •Requires solving a nonlinear equation for general MFs
- •Less intuitive than centroid
Edge cases and pitfalls
Confusing bisector with centroid for asymmetric TFNs - they differ.
For trapezoidal FNs, always check which half contains the bisector before applying the formula.
Works with
How to cite
van Leekwijck, W.; Kerre, E.E. (1999). Defuzzification: criteria and classification. Fuzzy Sets and Systems. https://doi.org/10.1016/S0165-0114(97)00337-0
System ID, as it appears in reports and the API
DEFUZZ-BISECTOR