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Weight Subjective
FUZZY-DEMATEL - Fuzzy Decision Making Trial and Evaluation Laboratory (CFCS, defuzzify-first)
Fuzzy cause-effect influence network (CFCS-defuzzified total relation matrix) for criteria weighting
Gabus, A., Fontela, E.1972
Overview
FUZZY-DEMATEL returns crisp criterion weights (Σ w_j = 1, w_j ≥ 0) from a fuzzy cause-effect analysis. Experts give triangular-fuzzy direct-influence judgements on a linguistic scale; the matrix is CFCS-defuzzified, normalised, and the total-relation matrix yields prominence (D+R) and relation (D−R). The weight of each criterion is its normalised prominence; D−R (>0 cause, <0 effect) describes its causal role.
- Output
- Weight, higher is better
- Data
- Fuzzy (TFN), complete numeric matrix
- Weights
- Derived internally, no weight source needed
- Size
- 2+ alternatives, 3-12 criteria works best
- Used for
- Causal analysis, criteria interdependence
Look elsewhere when
- •No data variation (constant criterion). Weight degenerates.
- •Expert judgment is the actual driver. Use subjective weighting.
Assumptions to verify
- Decision matrix exists with measurable criteria
- Sufficient inter-alternative variation per criterion
Edge cases and pitfalls
The influence matrix is asymmetric - ã_ij (i influences j) and ã_ji are independent.
Weight here is normalised prominence (Eq.15); this differs from the ‖(D+R,D−R)‖₂ form used by crisp DEMATEL in this platform.
Works with
Its derived weights can feed
How to cite
Gabus, A.; Fontela, E. (1972). World problems, an invitation to further thought within the framework of DEMATEL. Battelle Geneva Research Centre.
System ID, as it appears in reports and the API
FUZZY-DEMATEL