Interaction between criteria through the use of fuzzy measures
Jean‐Luc Marichal · Open Repository and Bibliography (University of Luxembourg) · 1996
Interaction between criteria ln classical MCDM procedures (ELECTRE & PROMETHEE ...) we consider additive weights : p( i) related to criterion i such that L p(i) == 1 i==l,...,n in aIder to introduce compensation via weighted sums in aggregation phase:C( b) ~( ' ) (i) + == a, == LIlI P 'l r ab == Pab + Pab i==l,...,n r(i) == 1 if a >.b ab -'lt == 0 otherwise.~(1,... ,n) == 1 Additive model : ~(i, j) == ~(i) + ~(j) ~(i) == p( i). 1 .1This model cali be extended in a Choquet capacity (fuzzy measure, Sugeno measure) : X : set of criteria P(X): power set of X Ji, : P(X) -+ [0, 1] Ji,(P.)~ 0, P E P(X) Ji,(0) == 0 Ji, (X) == 1 (not corn pulsary) Ji,(Q) ~ Ji,(P) if Q ç P