WINGS - Weighted Influence Non-linear Gauge System

Influence network weighting + DEMATEL-style strength scoring

Michnik, J.2013doi:10.1016/j.ejor.2013.02.007 ↗

Overview

P_i (prominence) measures total influence - how much a criterion both sends and receives influence. E_i (relation) distinguishes cause (E>0, net sender) from effect (E<0, net receiver). WINGS extends DEMATEL by incorporating criterion strength (intensity/importance) separately from influence (direction/flow). The output is primarily used for criteria weighting and causal map construction, not directly for alternative ranking.

Output: weight or utility, higher is better
Data: Crisp, complete numeric matrix
Weights: Derived internally, no weight source needed
Size: 2+ alternatives, 3-12 criteria works best
Used for: General MCDM

How it works

1
Strength matrix B (self-influence on diagonal, pairwise influence off-diagonal).
$B = [b_{ij}]_{n \times n}, b_{ii} = strength, b_{ij} = influence$
Michnik 2013, p.140 Eq.(1)
2
Normalise C = B/s with s = Σ_i Σ_j b_ij.
$C = \frac{B}{\sum _{i, j} b _{ij}}$
Michnik 2013, p.141 Eq.(2)
3
Total relation T = C(I − C)^{−1}.
$T = C (I - C)^{- 1}$
Michnik 2013, p.141 Eq.(3)
4
Engagement r_i + c_i and role r_i − c_i; weights from engagement.
$r_{i} = j \sum t_{ij}, c_{i} = j \sum t_{j i}; w_{i} = \frac{r _{i} + c _{i}}{\sum _{k} ( r _{k} + c _{k} )}$
Michnik 2013, p.142 Eqs.(4)-(5)

Fits when

•Native group-decision support (multi-DM aggregation built into the pipeline)

Edge cases and pitfalls

(I − X) must be invertible - this requires the spectral radius of X to be < 1.

Works with

Its derived weights can feed

AHPSORTAPLOCO ARAS AROMAN ARTASI COBRA COCOSO CODAS COMPROMISE-PROGRAMMING COPRAS CRADIS DEA DEA-CROSSEFF DNMA EDAS ELECTRE ELECTRE-I ELECTRE-II ELECTRE-III ELECTRE-IVELECTRE-TRIELECTRE-TRI-BEVAMIX EXPROM-I EXPROM-II FMEA FUCA GOAL-PROGRAMMING GRA HELLWIG IDOCRIW LINMAP LMAW MABAC MAIRCA MARA MARCOS MAUT MOORA MULTIMOORA NAIADE OCRA ORESTE PAM PAMSSEM-I PAMSSEM-II PROMETHEE PROMETHEE-I PROMETHEE-III PSI QUALIFLEX RAFSI RAPS RAT RAWEC REGIME RIM ROV SAW SECA SIR SMART SPOTIS TAXONOMY TODIM TOPSISTOPSIS-SORTUTAUTADISUTASTAR VIKOR WASPAS WEBIRA WEDBA WISP WPM

How to cite

Michnik, J. (2013). Weighted Influence Non-linear Gauge System (WINGS) - An analysis method for the systems of interrelated components. European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2013.02.007

BibTeX RIS APA (.txt)DOI ↗

System ID, as it appears in reports and the API

WINGS

Overview

Output

weight or utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

General MCDM

How it works

Strength matrix B (self-influence on diagonal, pairwise influence off-diagonal).

B = [b_{ij}]_{n \times n}, b_{ii} = strength, b_{ij} = influence

Michnik 2013, p.140 Eq.(1)

Normalise C = B/s with s = Σ_i Σ_j b_ij.

C = \frac{B}{\sum _{i, j} b _{ij}}

Michnik 2013, p.141 Eq.(2)

Total relation T = C(I − C)^{−1}.

T = C (I - C)^{- 1}

Michnik 2013, p.141 Eq.(3)

Engagement r_i + c_i and role r_i − c_i; weights from engagement.

r_{i} = j \sum t_{ij}, c_{i} = j \sum t_{j i}; w_{i} = \frac{r _{i} + c _{i}}{\sum _{k} ( r _{k} + c _{k} )}

Michnik 2013, p.142 Eqs.(4)-(5)

How to cite

BibTeX RIS APA (.txt)DOI ↗

System ID, as it appears in reports and the API

WINGS