Counting non-isomorphic maximal independent sets of the n-cycle graph

The number of maximal independent sets of the n-cycle graph C_n is known to be the nth term of the Perrin sequence. The action of the automorphism group of C_n on the family of these maximal independent sets partitions this family into disjoint orbits, which represent the non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets. We provide exact formulas for the total number of orbits and the number of orbits having a given number of isomorphic representatives. We also provide exact formulas for the total number of unlabeled (i.e., defined up to a rotation) maximal independent sets and the number of unlabeled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences.Comment: Revised versio

Preference aggregation with multiple criteria of ordinal significance

In this paper we address the problem of aggregating outranking situations in the presence of multiple preference criteria of ordinal significance. The concept of ordinal concordance of the global outranking relation is defined and an operational test for its presence is developed. Finally, we propose a new kind of robustness analysis for global outranking relations taking into account classical dominance, ordinal and classical majority oncordance in a same bipolar-valued logical framewor

On a natural fuzzification of Boolean logic

In this communication we propose two logically sound fuzzification and defuzzifi- cation techniques for implementing a credibility calculus on a set of propositional expressions. Both rely on a credibility evaluation domain using the rational in- terval [−1, 1] where the sign carries a split truth/falseness denotation. The first technique implements the classic min and max operators where as the second technique implements Bochvar-like operators. Main interest in the communica- tion is given to the concept of natural fuzzification of a propositional calculus. A formal definition is proposed and the demonstration that both fuzzification techniques indeed verify this definition is provided

Etudes universitaires sur le Luxembourg: Mots d'accueil

Concise historical review of 20 years of interdisciplinary Luxembourg studies before the foundation of the University of Luxembour

On linear decompositions of L-valued simple graphs

In this report we will present a linear decomposition of a given L- valued binary relation into a set of sub-relations of kernel-dimension one. We will apply this theoretical result to the design of a faster algorithm for computing L-valued kernels on general L-valued simple graphs

UL HPC users'session: Mastering big data

We illustrate in this presentation an optimized HPC implementation for outranking digraphs of huge orders, up to several millions of decision alternatives. The proposed outranking digraph model is based on a quantiles equivalence class decomposition of the underlying multicriteria performance tableau. When locally ranking each of these ordered components, we may readily obtain an overall linear ranking of big sets of decision alternatives. The proposed optimization strategies tackles algorithmic refinements of the ranking algorithm, reducing the size of python data objects, typing the data for efficient cython and C compilation, efficient sharing of static data via global python variables, using a multiprocessing task queue, and, last but not least, use the efficient UL HPC equipements

On maximal independent sets in circulant digraphs

In this research note we introduce St-Nicolas graphs, i.e. circulant digraphs showing exactly n maximal independent sets, isomorph under the digraph’s automorphisms group. This class of digraphs represent a generalisation of Andrásfai graphs with interesting links to finite group theory.Final versio

On computing kernels on fuzzy simple graphs by combinatorial enumeration using a CPL(FD) system

This paper reports our communication done at the 8th Benelux Workshop on Logic Programming in Louvain-la-Neuve, 9 September 1996. We present a constraint formulation in finite domains of the kernel construction on simple digraphs and give some comments on implementation in CHIP. Application to fuzzy choice procedures will illustrate the theoretical developments

Bipolar ranking from pairwise fuzzy outrankings

In this paper we propose to apply the concept of L-valued kernels to the problem of constructing a global ranking from a pairwise L-valued outranking relation defined on a set of decision alternatives as encountered in the fuzzy preference modelling context. Our approach is based on a repetitive selection of best and worst candidates from sharpest L-valued or most credible initial and terminal kernels. A practical illustration will concern the global ranking of movies from individual evaluations of a given set of movie critics