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Ranking
IV-PROJECTION - Interval-Valued Intuitionistic Fuzzy Projection-based MCDM
IVIFS projection-based ranking
Yue, Z.2019doi:10.1007/S00521-018-3571-5 ↗
Overview
IV-PROJECTION ranks alternatives by the Yue (2019) normalized projection measure NP(A_i, A+) for IVIFS data. Membership/non-membership tuples enter the inner product directly; ranking is by descending NP.
- Output
- utility, higher is better
- Data
- Interval Intuitionistic Fuzzy, ivifs tuples complete
- Weights
- Needs a weight source
- Size
- 2+ alternatives, 3-10 criteria works best
- Used for
- IVIFS group MCDM, knowledge transfer effectiveness (Yue 2019), patent quality evaluation (Xie 2025), expert-driven evaluation under epistemic uncertainty
Fits when / Look elsewhere when
Fits when
- •Captures both distance and angle to ideal solution (projection geometry)
- •Avoids defuzzification information loss (operates directly on IVIFS algebra)
- •Native support for group decision making via averaging over decision-maker matrices
- •Linear-time per criterion; lightweight compared with LP-based methods
Look elsewhere when
- •Crisp data sufficient - use base PROJECTION/TOPSIS directly
- •Preference-disaggregation needed - use UTA-family
- •Stochastic uncertainty dominates - use STOCHASTIC-UTA
Assumptions to verify
- IVIFS axiom muU + nuU ≤ 1 holds for every cell
- Criterion directions correctly labelled (max/min) before PIS construction
- All experts use the same IVIFS-linguistic conversion table
Limitations
- •Requires IVIFS evaluations (often elicited via expert linguistic-to-IVIFS translation tables)
- •Sensitive to PIS construction choice (benefit ⟨[1,1],[0,0]⟩ vs. data-driven max)
- •Does not model preference structure explicitly (use UTA-family if preference-disaggregation needed)
Edge cases and pitfalls
- •Zero-norm alternative (all cells = ⟨[0,0],[0,0]⟩): NP undefined; degenerate alternative - flag and skip.
- •Identical alternatives: equal NP → tie-break by alternative_id argsort.
- •muU + nuU > 1 violation: rejected by E-2 (IVIFS axiom).
Forgetting to flip the PIS cell for cost criteria (use ⟨[0,0],[1,1]⟩, not ⟨[1,1],[0,0]⟩).
Confusing un-normalized projection (Proj) with the normalized projection (NP) used for ranking.
Using a TFN or interval cell instead of an IVIFS 4-tuple; value-space mismatch breaks E-2.
Works with
How to cite
Yue, Z. (2019). An interval-valued intuitionistic fuzzy projection-based approach and application to evaluating knowledge transfer effectiveness. Neural Computing and Applications. https://doi.org/10.1007/S00521-018-3571-5
System ID, as it appears in reports and the API
IV-PROJECTION