On the Mathematical Foundation of MACBETH

Multi-objective optimization and multi-criteria decision aid applied to the design of 3D-stacked integrated circuits

“…Wire of a few millimetres long can be replaced by TSV of a few tens of microns, as shown in Figure 1.4. These shorter interconnections will introduce shorter delays, hence allowing higher working frequencies [5,17]. [5] Silicon efficiency and accessibility Adding a vertical dimension allows to increase the integration density.…”

“…For instance, we can mention Multi-Attribute Utility Theory (MAUT) [13], Analytical Hierarchy Process (AHP) [14], ELECTRE [15], PROMETHEE [16], MACBETH [17], etc.…”

“…The latter has been often cited as the most prominent one as it is based on the current technologies and still uses silicon as basis material; 3D-SICs can also allow shorter interconnection lengths, smaller footprint, larger bandwidth, heterogeneous circuits among their main advantages [5,[16][17][18].…”

Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method

“…We will use, however, the preference model (1 ′ ) with normalization constraints bounding U(x) to the interval [0,1].…”

“…It is, however, necessary that the above categories correspond to disjoint intervals (represented in terms of the real numbers). The bounds for such intervals should not be arbitrarily fixed a priori, they should be compatible simultaneously with the numerical values of all particular actions from A, so as to ensure compatibility between these values (see Bana e Costa et al 2005). Linear programming models are used for these calculations.…”