Choquet integral, additive value functions and weighted sum: comparing expressiveness

Short description

This workflow compares the expressiveness of a Choquet integral, a weighted sum and additive value functions, created for the URPDM2010 conference in Coimbra, Portugal.

Detailed description

This workflow generates a number of alternatives by drawing at random a vector of evaluations for each of them via the randomNormalizedPerformanceTable component and a random order on these alternatives is drawn via the randomAlternativesRanks component. Then we examine whether this order is representable by a simple weighted sum (additiveValueFunctionsIdentification with 1 segment) a Choquet integral with respect to a 2 additive capacity (linProgCapaIdent with k=2), a piecewise-linear additive value function with 2 pieces (additiveValueFunctionsIdentification with 2 segments) or a general additive value function.

The outputs are then pairwisely compared via Kendall’s Tau coefficient.

This example is inspired from [PirlotSchmitzMeyer2010].




[PirlotSchmitzMeyer2010]Pirlot M, Schmitz H, Meyer P, An empirical comparison of the expressiveness of the additive value function and the Choquet integral models for representing rankings. Proc. of 25th Mini-EURO Conference “Uncertainty and Robustness in Planning and Decision Making” (URPDM 2010), Coimbra, Portugal, 15-17 April 2010 (preliminary pdf).