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Defuzzification
Score Function Defuzzification - Crisp ranking score for IFN/PFN/q-ROFS families
Defuzzification operator - score and accuracy functions for membership-nonmembership pairs
Chen, S.M., Tan, J.M.1994doi:10.1016/0165-0114(94)90084-1 ↗
Overview
Always match score formula to fuzzy type: IFN→μ-ν, PFN→μ²-ν², q-ROFS→μ^q-ν^q. Use accuracy h as tiebreaker. Report both s and h in output table. Use Liu & Wang rescaling to [0,1] when chaining to normalisation-sensitive methods.
- Output
- crisp score, higher is better
- Data
- Intuitionistic Fuzzy, ifn pfn pairs
- Size
- 1+ alternatives
- Used for
- IFN MCDM, PFN MCDM, q-ROFS MCDM, IF-TOPSIS, PF-TOPSIS
Fits when / Look elsewhere when
Fits when
- •Unified formula for q-ROFS family
- •Accuracy tiebreaker handles degenerate cases
- •Widely used in MCDM literature
Look elsewhere when
- •TFN/Gaussian inputs - wrong type
Assumptions to verify
- Fuzzy type selected matches input data (IFN/PFN/q-ROFS)
- Membership constraint μ^q+ν^q ≤ 1 satisfied
Limitations
- •Score is 1D - loses hesitancy information from 2D pair
- •Equal score+accuracy → true tie, no further ranking
Edge cases and pitfalls
Using IFN score (μ-ν) for PFN data - wrong. Use μ²-ν² for PFN.
Forgetting accuracy tiebreak when scores are equal - leads to arbitrary ordering.
Applying s without checking μ^q+ν^q ≤ 1 constraint first.
Works with
How to cite
Chen, S.M.; Tan, J.M. (1994). Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems. https://doi.org/10.1016/0165-0114(94)90084-1
System ID, as it appears in reports and the API
DEFUZZ-SCORE-IFN