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Defuzzification
Mean of Maxima (MOM) Defuzzification - Crisp value at the plateau of maximum membership
Defuzzification operator - mean of maxima
Lee, C.C.1990doi:10.1109/21.52551 ↗
Overview
MOM = modal value = b for TFN. Fast and simple. Ignores spread (a and c). Use when the most likely value is the only relevant information and tails are not informative.
- 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
- •Simple: x*=b for TFN
- •Fast computation
- •Intuitive (most likely value)
Look elsewhere when
- •When spread information is important (use centroid)
Assumptions to verify
- Input is a valid TFN or trapezoidal FN
Limitations
- •Ignores spread completely
- •Can give low-membership midpoint for trapezoidal with b≠c
Edge cases and pitfalls
Using MOM when the fuzzy set is asymmetric - centroid is more representative in that case.
Applying MOM to a bimodal MF - the mean of two separate peaks may have low membership.
Works with
How to cite
Lee, C.C. (1990). Fuzzy logic in control systems: fuzzy logic controller, Part I. IEEE Transactions on Systems, Man, and Cybernetics. https://doi.org/10.1109/21.52551
System ID, as it appears in reports and the API
DEFUZZ-MOM