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

The Epidemiology of Vertigo, Dizziness, and Unsteadiness and Its Links to Co-Morbidities

Vertigo, dizziness, and unsteadiness (VDU) are common symptoms traditionally considered to result from different kinds of vestibular and non-vestibular dysfunctions. The epidemiology of each symptom and how they relate to each other and to migraine, agoraphobia, motion sickness susceptibility (MSS), vaso-vagal episodes (VVE), and anxiety-depression was the object of this population-based study in north-eastern France. A self-administered questionnaire was returned by 2987 adults (age span 18–86 years, 1471 women). The 1-year prevalence for vertigo was 48.3%, for unsteadiness 39.1%, and for dizziness 35.6%. The three symptoms were correlated with each other, occurred mostly (69.4%) in various combinations rather than in isolation, less than once per month, and 90% of episodes lasted ≤2 min. The three symptoms were similar in terms of female predominance, temporary profile of the episodes, and their link to falls and nausea. Symptom episodes of >1 h increase the risk of falls. VDU are much more common than the known prevalence of vestibular disorders. The number of drugs taken increase VDU even when controlling for age. Each VDU symptom was correlated with each co-morbidity in Chi-squared tests. The data suggest that the three symptoms are more likely to represent a spectrum resulting from a range of similar – rather than from different, unrelated – mechanisms or disorders. Logistic regressions controlling for each vestibular symptom showed that vertigo correlated with each co-morbidity but dizziness and unsteadiness did not, suggesting that vertigo is certainly not a more specific symptom than the other two. A logistic regression using a composite score of VDU, controlling for each co-morbidity showed a correlation of VDU to migraine and VVE but not to MSS and not to agoraphobia in men, only in women

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

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 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

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

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