PIF-DOMBI - Picture Fuzzy Dombi Aggregation Operators for MADM (Jana, Senapati, Pal & Yager 2019)

Dombi t-norm/t-conorm aggregation on Picture Fuzzy Numbers (PFN: μ,η,ν; μ+η+ν≤1). PFDWA (arithmetic, Def.13/Eq.2) primary, PFDWG (geometric, Def.16/Eq.7) companion. Ranking by score Ê(T)=(1+μ-ν)/2 (Def.6) with accuracy L̂(T)=μ-ν tie-break (Def.7).

Jana, C., Senapati, T., Pal, M., Yager, R. R.2019doi:10.1016/j.asoc.2018.10.021 ↗

Overview

PIF-DOMBI applies the Jana et al. 2019 Picture Fuzzy Dombi aggregation family. Choose PFDWA (default, arithmetic, Eq.2) for compensatory aggregation or PFDWG (Eq.7) for geometric (less compensatory, low μ values penalized more). The ℜ ≥ 1 parameter controls trade-off: ℜ→1 approaches algebraic t-norm, ℜ→∞ approaches max/min. Score Ê(T)=(1+μ-ν)/2 ignores η (refusal/neutral); if η-sensitivity matters, prefer Wei 2017 PFWA or Cuong-Kreinovich score variants.

Data: Picture Fuzzy
Weights: Needs a weight source

Edge cases and pitfalls

Value-space violation: ensure every input cell satisfies PFN (μ+η+ν ≤ 1 strictly) before computation.
Boundary pole (0 or 1) causes division-by-zero in Dombi; clip to (eps, 1-eps) with eps=1e-9 if your data has hard boundaries.
PFDWA ≠ PFDWG: arithmetic and geometric variants typically yield different rankings, especially with skewed η distributions. Document operator_choice in the report.
Bu manifestin B.extensions bloğunda kaynak gösterilen Wei (2017), 'Picture fuzzy aggregation operators...' (DOI 10.3233/JIFS-161798) GERİ ÇEKİLMİŞTİR (RETRACTED); bu kaynağı PFWA/agregasyon gerekçesi olarak KULLANMAYIN.

How to cite

Jana, C.; Senapati, T.; Pal, M.; Yager, R. R. (2019). Picture fuzzy Dombi aggregation operators: Application to MADM process. Applied Soft Computing. https://doi.org/10.1016/j.asoc.2018.10.021

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System ID, as it appears in reports and the API

PIF-DOMBI

PIF-DOMBI - Picture Fuzzy Dombi Aggregation Operators for MADM (Jana, Senapati, Pal & Yager 2019)

Overview

Data

Picture Fuzzy

Weights

Needs a weight source

Edge cases and pitfalls

Value-space violation: ensure every input cell satisfies PFN (μ+η+ν ≤ 1 strictly) before computation.

Boundary pole (0 or 1) causes division-by-zero in Dombi; clip to (eps, 1-eps) with eps=1e-9 if your data has hard boundaries.

PFDWA ≠ PFDWG: arithmetic and geometric variants typically yield different rankings, especially with skewed η distributions. Document operator_choice in the report.

Bu manifestin B.extensions bloğunda kaynak gösterilen Wei (2017), 'Picture fuzzy aggregation operators...' (DOI 10.3233/JIFS-161798) GERİ ÇEKİLMİŞTİR (RETRACTED); bu kaynağı PFWA/agregasyon gerekçesi olarak KULLANMAYIN.