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Defuzzification
Alpha-Cut Defuzzification - Crisp interval or representative via α-level cut
Defuzzification operator - alpha-cut crisp approximation
Zadeh, L.A.1965doi:10.1016/S0019-9958(65)90241-X ↗
Overview
α=0.5 midpoint (a+2b+c)/4 is the most common MCDM choice. Report results for multiple α values to assess sensitivity. Higher α → more weight on the modal value b. λ > 0.5 → optimistic DM attitude.
- Output
- crisp score, higher is better
- Data
- Fuzzy (TFN), fuzzy numbers
- Size
- 1+ alternatives
- Used for
- Fuzzy MCDM, interval fuzzy MCDM, Z-number MCDM
Fits when / Look elsewhere when
Fits when
- •Parametric: α controls confidence, λ controls attitude
- •Common formula (a+2b+c)/4 is widely cited
- •Interval output retains uncertainty at choice of DM
Look elsewhere when
- •When α cannot be determined - use centroid instead
Assumptions to verify
- α level is meaningful for the problem
- TFN satisfies a ≤ b ≤ c
Limitations
- •Requires specifying α and λ (subjective)
- •Different (α,λ) choices yield different rankings
Edge cases and pitfalls
Confusing (a+2b+c)/4 (α-cut midpoint at α=0.5) with centroid (a+b+c)/3 - different results for asymmetric TFNs.
Applying α=0 which gives [a,c] (interval, not scalar) - must use a scalar conversion rule.
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-ALPHA-CUT