IRIS Plugin for Decision Deck Vincent Mousseau, Salem Chakhar - - PowerPoint PPT Presentation

Electre Tri method and related concepts The IRIS Plugin

IRIS Plugin for Decision Deck

Vincent Mousseau, Salem Chakhar

Lamsade, Universit´ e Paris Dauphine, UMR CNRS 7024

June 15, 2008

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

1

Electre Tri method and related concepts Electre Tri method / Assignment examples Inference procedure Robust Assignment of alternatives Inconsistency Analysis

2

The IRIS Plugin

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Sorting problems / Electre Tri method

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Sorting problems / Electre Tri method

. . .

Class 1 Class 2 Class k

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Sorting problems / Electre Tri method

. . .

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method

1

Define categories as limit profiles B = {b1, b2, . . . , bp},

C1 C2 Cp−1 Cp Cp+1 bp b0 bp+1 bp−1 b1 g1 g2 g3 gm−1 gm

2

Compare a to b1, b2, ..., bp using an outranking relation S.

3

Assign a to the highest Ch for which aSbh−1 and ¬(aSbh).

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method

1

Define categories as limit profiles B = {b1, b2, . . . , bp},

C1 C2 Cp−1 Cp Cp+1 bp b0 bp+1 bp−1 b1 g1 g2 g3 gm−1 gm

2

Compare a to b1, b2, ..., bp using an outranking relation S.

3

Assign a to the highest Ch for which aSbh−1 and ¬(aSbh).

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method

1

Define categories as limit profiles B = {b1, b2, . . . , bp},

C1 C2 Cp−1 Cp Cp+1 bp b0 bp+1 bp−1 b1 g1 g2 g3 gm−1 gm

2

Compare a to b1, b2, ..., bp using an outranking relation S.

3

Assign a to the highest Ch for which aSbh−1 and ¬(aSbh).

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method / Assignment examples

We consider Electre Tri to model DMs preferences, preference parameters = {weights, category limits, vetos} Input I= assignment examples such that a → [Cmin(a), Cmax(a)], ∀a ∈ A∗ ⊂ A If categ. limits and vetos are known, I leads to linear constraints on weights, Ω = {weights} and I ⇒ Ω(I) ⊂ Ω Inference : select ω∗ ∈ Ω(I), Robust assignment : [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) Inconsistency analysis : when Ω(I) = ∅, how to modify I to make Ω(I) non empty

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method / Assignment examples

We consider Electre Tri to model DMs preferences, preference parameters = {weights, category limits, vetos} Input I= assignment examples such that a → [Cmin(a), Cmax(a)], ∀a ∈ A∗ ⊂ A If categ. limits and vetos are known, I leads to linear constraints on weights, Ω = {weights} and I ⇒ Ω(I) ⊂ Ω Inference : select ω∗ ∈ Ω(I), Robust assignment : [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) Inconsistency analysis : when Ω(I) = ∅, how to modify I to make Ω(I) non empty

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method / Assignment examples

We consider Electre Tri to model DMs preferences, preference parameters = {weights, category limits, vetos} Input I= assignment examples such that a → [Cmin(a), Cmax(a)], ∀a ∈ A∗ ⊂ A If categ. limits and vetos are known, I leads to linear constraints on weights, Ω = {weights} and I ⇒ Ω(I) ⊂ Ω Inference : select ω∗ ∈ Ω(I), Robust assignment : [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) Inconsistency analysis : when Ω(I) = ∅, how to modify I to make Ω(I) non empty

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method / Assignment examples

We consider Electre Tri to model DMs preferences, preference parameters = {weights, category limits, vetos} Input I= assignment examples such that a → [Cmin(a), Cmax(a)], ∀a ∈ A∗ ⊂ A If categ. limits and vetos are known, I leads to linear constraints on weights, Ω = {weights} and I ⇒ Ω(I) ⊂ Ω Inference : select ω∗ ∈ Ω(I), Robust assignment : [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) Inconsistency analysis : when Ω(I) = ∅, how to modify I to make Ω(I) non empty

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method / Assignment examples

We consider Electre Tri to model DMs preferences, preference parameters = {weights, category limits, vetos} Input I= assignment examples such that a → [Cmin(a), Cmax(a)], ∀a ∈ A∗ ⊂ A If categ. limits and vetos are known, I leads to linear constraints on weights, Ω = {weights} and I ⇒ Ω(I) ⊂ Ω Inference : select ω∗ ∈ Ω(I), Robust assignment : [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) Inconsistency analysis : when Ω(I) = ∅, how to modify I to make Ω(I) non empty

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Electre Tri method / Assignment examples

We consider Electre Tri to model DMs preferences, preference parameters = {weights, category limits, vetos} Input I= assignment examples such that a → [Cmin(a), Cmax(a)], ∀a ∈ A∗ ⊂ A If categ. limits and vetos are known, I leads to linear constraints on weights, Ω = {weights} and I ⇒ Ω(I) ⊂ Ω Inference : select ω∗ ∈ Ω(I), Robust assignment : [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) Inconsistency analysis : when Ω(I) = ∅, how to modify I to make Ω(I) non empty

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inference procedures

Assignment examples I Inference procedure inferred parameters : ω∗(I) (P, ω∗(I)) = preference model that “best” match I

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inference procedure for Electre Tri

We consider an assignment examples a →DM Cha,a ∈ A Electre Tri assigns a to Cha iff aSbha−1 and ¬(aSbha), iff S(a, bha−1) ≥ λ and S(a, bha) < λ, iff

j:aSjbha−1 wj ≥ λ and

• j:aSjbha wj < λ

Consider slack variables xa and ya defined as S(a, bha−1) − xa = λ and S(a, bha) + ya + ε = λ. If xa ≥ 0 and ya ≥ 0, Electre Tri assigns a to Cha Maximize the minimum of xa ≥ 0 and ya ≥ 0, for all assignment examples.

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inference procedure for Electre Tri

We consider an assignment examples a →DM Cha,a ∈ A Electre Tri assigns a to Cha iff aSbha−1 and ¬(aSbha), iff S(a, bha−1) ≥ λ and S(a, bha) < λ, iff

j:aSjbha−1 wj ≥ λ and

• j:aSjbha wj < λ

Consider slack variables xa and ya defined as S(a, bha−1) − xa = λ and S(a, bha) + ya + ε = λ. If xa ≥ 0 and ya ≥ 0, Electre Tri assigns a to Cha Maximize the minimum of xa ≥ 0 and ya ≥ 0, for all assignment examples.

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inference procedure for Electre Tri

We consider an assignment examples a →DM Cha,a ∈ A Electre Tri assigns a to Cha iff aSbha−1 and ¬(aSbha), iff S(a, bha−1) ≥ λ and S(a, bha) < λ, iff

j:aSjbha−1 wj ≥ λ and

• j:aSjbha wj < λ

Consider slack variables xa and ya defined as S(a, bha−1) − xa = λ and S(a, bha) + ya + ε = λ. If xa ≥ 0 and ya ≥ 0, Electre Tri assigns a to Cha Maximize the minimum of xa ≥ 0 and ya ≥ 0, for all assignment examples.

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inference procedure for Electre Tri

We consider an assignment examples a →DM Cha,a ∈ A Electre Tri assigns a to Cha iff aSbha−1 and ¬(aSbha), iff S(a, bha−1) ≥ λ and S(a, bha) < λ, iff

j:aSjbha−1 wj ≥ λ and

• j:aSjbha wj < λ

Consider slack variables xa and ya defined as S(a, bha−1) − xa = λ and S(a, bha) + ya + ε = λ. If xa ≥ 0 and ya ≥ 0, Electre Tri assigns a to Cha Maximize the minimum of xa ≥ 0 and ya ≥ 0, for all assignment examples.

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inference procedure for Electre Tri

Max α s.c. α ≤ xa, ∀a ∈ A∗ α ≤ ya, ∀a ∈ A∗ S(a, bha−1) − xa = λ, ∀a ∈ A∗ S(a, bha) + ya = λ, ∀a ∈ A∗ λ ∈ [0.5, 1]

• j∈F wj = 1, wj ≥ 0,

∀j ∈ F

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Robust Assignment of alternatives

Assignment examples ⇒ linear constraints on wj and λ ⇒ (wj, λ) ∈ Ω(I) If there ∃ω ∈ Ω(I) such that a →ω Ch, then Ch is a possible assignment for a considering I, Compute [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) the range of possible assignment for a considering I,

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Robust Assignment of alternatives

Assignment examples ⇒ linear constraints on wj and λ ⇒ (wj, λ) ∈ Ω(I) If there ∃ω ∈ Ω(I) such that a →ω Ch, then Ch is a possible assignment for a considering I, Compute [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) the range of possible assignment for a considering I,

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Robust Assignment of alternatives

Assignment examples ⇒ linear constraints on wj and λ ⇒ (wj, λ) ∈ Ω(I) If there ∃ω ∈ Ω(I) such that a →ω Ch, then Ch is a possible assignment for a considering I, Compute [Cmin(a), Cmax(a)], a ∈ A \ A∗ s.t. Ω(I) the range of possible assignment for a considering I,

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Each assignment example ⇒ 2 linear constraints on wj and λ, If the examples do not match Electre Tri, the set Ω(I) of admissible values for wj and λ is empty → inconsistency When Ω(I) = ∅, how to modify I to make Ω(I) non empty? I1 ⊂ I I2 ⊂ I I3 ⊂ I ... Ik ⊂ I I inconsistent Inconsistency resolution

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Each assignment example ⇒ 2 linear constraints on wj and λ, If the examples do not match Electre Tri, the set Ω(I) of admissible values for wj and λ is empty → inconsistency When Ω(I) = ∅, how to modify I to make Ω(I) non empty? I1 ⊂ I I2 ⊂ I I3 ⊂ I ... Ik ⊂ I I inconsistent Inconsistency resolution

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Each assignment example ⇒ 2 linear constraints on wj and λ, If the examples do not match Electre Tri, the set Ω(I) of admissible values for wj and λ is empty → inconsistency When Ω(I) = ∅, how to modify I to make Ω(I) non empty? I1 ⊂ I I2 ⊂ I I3 ⊂ I ... Ik ⊂ I I inconsistent Inconsistency resolution

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Assignment examples define m constraints

       Σn

j=1α1jwj + α′ 1λ

≥ β1 . . . Σn

j=1α(m−1)jwj + α′ m−1λ

≥ βm−1 Σn

j=1αmjwj + α′ mλ

≥ βm [1]

I = {1, . . . , m} ; A subset S ⊂ I resolves [1] iff I \ S = ∅ We want to identify S1, S2, . . . , Sp ⊂ I such that :

(i) Si resolves [1], i ∈ {1, 2, ..., p}; (ii) Si Sj, i, j ∈ {1, ..., p}, i = j; (iii) |Si| ≤ |Sj|, i, j ∈ {1, 2, ..., p}, i < j;

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Assignment examples define m constraints

       Σn

j=1α1jwj + α′ 1λ

≥ β1 . . . Σn

j=1α(m−1)jwj + α′ m−1λ

≥ βm−1 Σn

j=1αmjwj + α′ mλ

≥ βm [1]

I = {1, . . . , m} ; A subset S ⊂ I resolves [1] iff I \ S = ∅ We want to identify S1, S2, . . . , Sp ⊂ I such that :

(i) Si resolves [1], i ∈ {1, 2, ..., p}; (ii) Si Sj, i, j ∈ {1, ..., p}, i = j; (iii) |Si| ≤ |Sj|, i, j ∈ {1, 2, ..., p}, i < j;

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Assignment examples define m constraints

       Σn

j=1α1jwj + α′ 1λ

≥ β1 . . . Σn

j=1α(m−1)jwj + α′ m−1λ

≥ βm−1 Σn

j=1αmjwj + α′ mλ

≥ βm [1]

I = {1, . . . , m} ; A subset S ⊂ I resolves [1] iff I \ S = ∅ We want to identify S1, S2, . . . , Sp ⊂ I such that :

(i) Si resolves [1], i ∈ {1, 2, ..., p}; (ii) Si Sj, i, j ∈ {1, ..., p}, i = j; (iii) |Si| ≤ |Sj|, i, j ∈ {1, 2, ..., p}, i < j;

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Let us define yi = 1 if constraint i is deleted = 0 sinon

P1      Min Σi∈Iyi s.t. Σn

j=1αijxj + α′ iλ + Myi ≥ βi, ∀i ∈ I

xj ≥ 0, j = 1..n, yi ∈ {0, 1}, i ∈ I

S1 = {i ∈ I : y ∗

i = 0} corresponds to (one of) the largest

subsets of constraints that resolve [1], Define P2 by adding to P1 the constraint

i∈S1 yi ≤ |S1| − 1,

we obtain S2 Proceed similarly to define P3, P4, ... and obtain S3, S4, ...

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Let us define yi = 1 if constraint i is deleted = 0 sinon

P1      Min Σi∈Iyi s.t. Σn

j=1αijxj + α′ iλ + Myi ≥ βi, ∀i ∈ I

xj ≥ 0, j = 1..n, yi ∈ {0, 1}, i ∈ I

S1 = {i ∈ I : y ∗

i = 0} corresponds to (one of) the largest

subsets of constraints that resolve [1], Define P2 by adding to P1 the constraint

i∈S1 yi ≤ |S1| − 1,

we obtain S2 Proceed similarly to define P3, P4, ... and obtain S3, S4, ...

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Let us define yi = 1 if constraint i is deleted = 0 sinon

P1      Min Σi∈Iyi s.t. Σn

j=1αijxj + α′ iλ + Myi ≥ βi, ∀i ∈ I

xj ≥ 0, j = 1..n, yi ∈ {0, 1}, i ∈ I

S1 = {i ∈ I : y ∗

i = 0} corresponds to (one of) the largest

subsets of constraints that resolve [1], Define P2 by adding to P1 the constraint

i∈S1 yi ≤ |S1| − 1,

we obtain S2 Proceed similarly to define P3, P4, ... and obtain S3, S4, ...

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Let us define yi = 1 if constraint i is deleted = 0 sinon

P1      Min Σi∈Iyi s.t. Σn

j=1αijxj + α′ iλ + Myi ≥ βi, ∀i ∈ I

xj ≥ 0, j = 1..n, yi ∈ {0, 1}, i ∈ I

S1 = {i ∈ I : y ∗

i = 0} corresponds to (one of) the largest

subsets of constraints that resolve [1], Define P2 by adding to P1 the constraint

i∈S1 yi ≤ |S1| − 1,

we obtain S2 Proceed similarly to define P3, P4, ... and obtain S3, S4, ...

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin Electre Tri method / Assignment examples Inference Robust Assignment Inconsistency Analysis

Inconsistency Analysis

Let us define yi = 1 if constraint i is deleted = 0 sinon

P1      Min Σi∈Iyi s.t. Σn

j=1αijxj + α′ iλ + Myi ≥ βi, ∀i ∈ I

xj ≥ 0, j = 1..n, yi ∈ {0, 1}, i ∈ I

S1 = {i ∈ I : y ∗

i = 0} corresponds to (one of) the largest

subsets of constraints that resolve [1], Define P2 by adding to P1 the constraint

i∈S1 yi ≤ |S1| − 1,

we obtain S2 Proceed similarly to define P3, P4, ... and obtain S3, S4, ...

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin

IRIS plugin

IRIS makes constructive learning of an Electre Tri model

• perational,

In IRIS, learning concerns the weights and cutting level (with veto), IRIS determines robust assignments, IRIS detects inconsistencies and propose alternative solution to restore consistency, Further version could integrate inference of the other parameters,

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin

IRIS plugin

Required input data

Category limits (gj(bh), qj(bh) et pj(bh)), Veto thresholds (vj(bh)), Assignment examples additional constraints on weights and cutting level λ.

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin

IRIS plugin

Information provided in absence of inconsistency : a central weight vector, for each alternative :

the assignment resulting from the use of the “central” weight vector, A robust assignment interval, i.e., [Cmin(a), Cmax(a)] for each Ch ∈ [Cmin(a), Cmax(a)], a weight vector compatible with the assignment,

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method and related concepts The IRIS Plugin

IRIS plugin

Information provided in presence of inconsistency : a central weight vector, for each alternative, the assignment resulting from the use of the “central” weight vector (possibly different from the assignment examples), a list of minimal subsets of assignment examples whose deletion would resolve inconsistency.

Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck