Additive Aggregation with Variable Interdependent Parameters: The VIP Analysis Software

Abstract

Abstract:We consider the aggregation of multicriteria performances by means of an additive value function under imprecise information. The problem addressed here is the way an analysis may be conducted when the decision makers are not able to (or do not wish to) fix precise values for the importance parameters. These parameters can be seen as interdependent variables that may take several values subject to constraints. First, we briefly classify some existing approaches to deal with this problem. We will argue that they complement each other, each one having its merits and shortcomings. Then, we present a new decision support software -VIP Analysis -which incorporates approaches belonging to different classes. It proposes a methodology of analysis based on the progressive reduction of the number of alternatives, introducing a concept of tolerance that lets the decision makers use some of the approaches in a more flexible manner.

Scale Dependence and Ranking Intervals in Additive Value Models Under Incomplete Preference Information

“…Alternative x 1 quasi-dominates x 2 if max V ∈ V x 2 −V x 1 ≤ , in which is a "small" predefined parameter (Dias and Climaco 2000). If = 0 05, then 1 2 quasi-dominates 2 1 , but not vice versa, in the example illustrated in Figure 1 with choice x + = 12 2 .…”

“…This has motivated the development of decision rules that offer recommendations about which nondominated alternative should be selected (e.g., Park and Kim 1997, Dias and Climaco 2000, Salo and Hämäläinen 2001. Many such rules compare magnitudes of value differences V x j − V x k across value functions in and seek to answer questions like, can the strength of preference for alternative x j over x k be greater than the strength of preference for x k over x j ?…”

“…To date, such difficulties arising from the lack of unequivocal numerical value differences have been addressed by considering only a subset of value functions in (e.g., Park and Kim 1997, Dias and Climaco 2000, Salo and Hämäläinen 2001. Specifically, value differences have been compared only within the set of representative value functions ⊂ such that any value function in is represented by one positive affine transformation that belongs to .…”

“…In other words, these recommendations depend on which value functions are chosen in the normalization phase to represent . Further examples of scale-dependent decision rules include quasi-dominance (Dias and Climaco 2000) and its derivatives (Sarabando and Dias 2009), absolute dominance (Salo and Hämäläinen 2001), the domain criterion (Eiselt and Laporte 1992), and the closely related measure acceptability index (Lahdelma et al 1998). Even sensitivity analyses based on computing the closest competitor (Rios Insua and French 1991) are scale dependent, as illustrated in Appendix A.…”

“…Many of these rules are based on comparisons of the magnitudes of the alternatives' value differences within a class of representative value functions, which includes all value functions that (i) are consistent with the stated preference information and, in addition, (ii) match the constraints that result from the chosen normalization of the value function (Park and Kim 1997, Dias and Climaco 2000, Salo and Hämäläinen 2001.…”