Multi-criteria analysis with partial information about the weighting coefficients

Abstract

In this paper we address the problem of ranking a set of alternatives with partial information about the weighting coefficients. We introduce a family of quasiorders that are easily interpretable and manageable, which includes among others, the natural quasiorder in R n and other well known preference structures in the literature. The enrichment of the preference structure with respect to the natural quasiorder is measured by means of an absolute measure we introduce.

The use of partial information on weights in multicriteria decision problems

“…These kinds of relations are easily interpretable in terms of minimum marginal substitution rates between the criteria, so they are easy for the decision maker to establish (Mármol, 1994;Carrizosa et al, 1995). Notice that the case of ordinal information with regard to the importance of the objectives is included because the matrices that represent ordinal information are always nonnegative inverse.…”

“…The new set of admissible weights is then P h,i (M)= {u L + , h 5 Mu 5i}. The approach that we present unifies the case of linear information concerning the importance of the objectives, studied in some particular cases, Mu ] h, by Carrizosa et al (1995) and the case of interval relations, h5 u 5i, addressed by Steuer (1976). It also generalizes the way in which the information may be supplied and makes it possible to deal with the general case.…”

“…A first approach consists of establishing intervals for the individual variation of weights (Steuer, 1976). In other cases, the decision maker may be able to give certain linear relations which express partial information about the marginal substitution rates between the criteria (Carrizosa et al, 1995).…”

Aggregation of ranked votes considering different relative gaps between rank positions

“…Other approaches to find the extreme points of S W have also been presented (Carrizosa et al, 1995;Mármol et al, 1998;Puerto et al, 2000;Mármol et al, 2002;Ahn, 2015).…”

Quasiconvex constrained multicriteria continuous location problems: Structure of nondominated solution sets

“…Other references devoted to study modifications of the Point-Objective location models are [3][4][5][6][7][8][9][10][11][12][13], among others. It is worth noting that from the above references only [3][4][5][6][7][8]11] consider the constrained case. Moreover, these references study the particular case of the Point-Objective location problem where distances are measured with the same norm.…”