MCDMDecision-makingDefuzzificationMath steps
Centroid Defuzzification — Centre of gravity crisp representative
DEFUZZ-CENTROID (Centroid Defuzzification — Centre of gravity crisp representative) is a defuzzification multi-criteria decision-making (MCDM) method introduced by Mamdani, E.H. in 1975. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
Key highlights
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
Intuition
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How it works
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When to use it
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.
Strengths & limitations
Strengths
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
Limitations
- Assumes full compensation — a strong score on one criterion can offset a weak score on another.
Common pitfalls
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Sources
- 1.Mamdani, E.H., Assilian, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies
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ScholarGate. (2026, June 2). DEFUZZ-CENTROID. ScholarGate. https://scholargate.app/decision-making/defuzz-centroid