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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Electre Tri method and related concepts 1 Electre Tri method / Assignment examples Inference procedure Robust Assignment of alternatives Inconsistency Analysis The IRIS Plugin 2 Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Sorting problems / Electre Tri method Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Sorting problems / Electre Tri method . . . Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Electre Tri method Define categories as limit profiles B = { b 1 , b 2 , . . . , b p } , 1 C p − 1 C p C p +1 C 1 C 2 g 1 g 2 g 3 g m − 1 g m b 0 b 1 b p − 1 b p b p +1 Compare a to b 1 , b 2 , ..., b p using an outranking relation S . 2 Assign a to the highest C h for which aSb h − 1 and ¬ ( aSb h ). 3 Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Electre Tri method Define categories as limit profiles B = { b 1 , b 2 , . . . , b p } , 1 C p − 1 C p C p +1 C 1 C 2 g 1 g 2 g 3 g m − 1 g m b 0 b 1 b p − 1 b p b p +1 Compare a to b 1 , b 2 , ..., b p using an outranking relation S . 2 Assign a to the highest C h for which aSb h − 1 and ¬ ( aSb h ). 3 Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Electre Tri method Define categories as limit profiles B = { b 1 , b 2 , . . . , b p } , 1 C p − 1 C p C p +1 C 1 C 2 g 1 g 2 g 3 g m − 1 g m b 0 b 1 b p − 1 b p b p +1 Compare a to b 1 , b 2 , ..., b p using an outranking relation S . 2 Assign a to the highest C h for which aSb h − 1 and ¬ ( aSb h ). 3 Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck

Electre Tri method / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 → [ C min ( a ) , C max ( 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 : [ C min ( a ) , C max ( 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 → [ C min ( a ) , C max ( 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 : [ C min ( a ) , C max ( 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 → [ C min ( a ) , C max ( 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 : [ C min ( a ) , C max ( 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 → [ C min ( a ) , C max ( 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 : [ C min ( a ) , C max ( 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 → [ C min ( a ) , C max ( 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 : [ C min ( a ) , C max ( 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 → [ C min ( a ) , C max ( 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 : [ C min ( a ) , C max ( 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin 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 / Assignment examples Electre Tri method and related concepts Inference The IRIS Plugin Robust Assignment Inconsistency Analysis Inference procedure for Electre Tri We consider an assignment examples a → DM C h a , a ∈ A Electre Tri assigns a to C h a iff aSb h a − 1 and ¬ ( aSb h a ), iff S ( a , b h a − 1 ) ≥ λ and S ( a , b h a ) < λ , iff � j : aS j b ha − 1 w j ≥ λ and � j : aS j b ha w j < λ Consider slack variables x a and y a defined as S ( a , b h a − 1 ) − x a = λ and S ( a , b h a ) + y a + ε = λ . If x a ≥ 0 and y a ≥ 0, Electre Tri assigns a to C h a Maximize the minimum of x a ≥ 0 and y a ≥ 0, for all assignment examples. Vincent Mousseau, Salem Chakhar IRIS Plugin for Decision Deck