On computing dominant and absorbent kernels in bipolar valued digraphs

7024 ANNALES DU LAMSADE N ° 6 Octobre 2006

In this paper we would like to thoroughly cover the problem of computing all kernels, i.e. minimal outranking and/or outranked independent choices in a bipolarvalued outranking digraph. First we introduce in detail the concept of bipolar-valued characterisation of outranking digraphs, choices and kernels. In a second section we present and discuss several algorithms for enumerating the kernels ...

Choices and kernels in bipolar valued digraphs

On the existence of (k, l)-kernels in infinite digraphs: A survey

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N , u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k− 1)-kernel. This work is a survey of results proving sufficient conditions for the exist...

1)-KERNELS IN STRONG k-TRANSITIVE DIGRAPHS

Let D = (V (D), A(D)) be a digraph and k ≥ 2 be an integer. A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N , we have d(u, v) ≥ k; it is l-absorbent if for every u ∈ V (D)−N , there exists v ∈ N such that d(u, v) ≤ l. A (k, l)-kernel of D is a k-independent and l-absorbent subset of V (D). A k-kernel is a (k, k − 1)-kernel. A digraphD is k-transitive if for any path ...

Exploitation of a bipolar-valued outranking relation for the choice of k best alternatives

This article presents the problem of the selection of k best alternatives in the context of multiple criteria decision aid. We situate ourselves in the context of pairwise comparisons of alternatives and the underlying bipolar-valued outranking digraph. We present three formulations for the best k-choice problem and detail how to solve two of them directly on the outranking digraph. Mots-Clefs....