Name
Abstract | ||
|---|---|---|
In this paper, we start from the premise that pairwise comparisons between alternatives can be modeled by means of the additive representation of preferences. In this setting we study some algebraic properties of three sets: the set of pairwise comparison matrices, its subset of consistent ones and the orthogonal complement of the latter. The three sets are all vector spaces and we propose and interpret simple bases for each one. We prove that a convenient inner product can be found in the three cases such that the corresponding basis is orthonormal with respect to the considered inner product. In addition (i) we prove that the well-known method of the logarithmic least squares used to estimate the weight vector can be reinterpreted by referring to a basis for the set of consistent preferences and (ii) we interpret a transformation recently proposed by Csató. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.ijar.2019.12.009 | International Journal of Approximate Reasoning |
Keywords | Field | DocType |
Pairwise comparisons,Multiplicative preference relations,Additive preference relations,Consistency,Analytic hierarchy process,Vector spaces | Least squares,Pairwise comparison,Discrete mathematics,Linear algebra,Vector space,Algebra,Matrix (mathematics),Weight,Orthonormal basis,Orthogonal complement,Mathematics | Journal |
Volume | Issue | ISSN |
118 | 1 | 0888-613X |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michele Fedrizzi | 1 | 342 | 20.01 |
| Matteo Brunelli | 2 | 303 | 17.62 |
| Alexandra Caprila | 3 | 0 | 0.34 |