We present in this paper a sparse 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. For the local rankings, both, Copeland's as well as the Net-Flows ranking rules, appear to give the best compromise between, on the one side, the fitness of the overall ranking with respect to the given global outranking relation and, on the other side, computational tractability for very big outranking digraphs modelling up to several trillions of pairwise outranking situations.

Cloud service providers (CSPs) offer different Service Level Agreements (SLAs) to the cloud users. Cloud Service Brokers (CSBs) provide multiple sets of alternatives to the cloud users according to users requirements. Generally, a CSB considers the service commitments of CSPs rather than the actual quality of CSPs services. To overcome this issue, the broker should verify the service performances while recommending cloud services to the cloud users, using all available data. In this paper, we compare our two approaches to do so: a min-max-min decomposition based on Intuitionistic Fuzzy Logic (IFL) and a Performance Heat Map technique, to evaluate the performance of commercially available cloud providers. While the IFL technique provides simple, total order of the evaluated CSPs, Performance Heat Map provides transparent and explanatoy, yet consistent evaluation of service performance of commercially available CSPs. The identified drawbacks of the IFL technique are: 1) It does not return the accurate performance evaluation overmultiple decision alternatives due to highly influenced by critical feedback of the evaluators; 2) Overall ranking of the CSPs is not as expected according to the performance measurement. As a result, we recommend to use performance Heat Map for this problem.

Selecting the appropriate cloud services and cloud providers according to the cloud users requirements is becoming a complex task, as the number of cloud providers increases. Cloud providers offer similar kinds of cloud services, but they are different in terms of price, quality of service, customer experience, and service delivery. The most challenging issue of the current cloud computing business is that cloud providers commit a certain Service Level Agreement (SLA), with cloud users, but there is little or no verification mechanisms which ensure that cloud providers are providing cloud services according to their commitment. In the current literature, there is a lack of an evaluation model which provides the real status of cloud providers for the cloud users. In this paper, an evaluation model is proposed, which verifies the quality of cloud services delivered for each service and provides the service status of the cloud providers. Finally, evaluation results obtained from cloud auditors are visualized in an ordered performance heat map, showing the cloud providers in a decreasing ordering of overall service quality. In this way, the proposed service quality evaluation model represents a visual recommender system for cloud service brokers and cloud users.

The chapter concerns the attribution of the EURO Best Poster Award at the 20^th EURO Conference, held in Rhodes, July 2004. We present the historical decision making process leading to the selection of the winner, followed by a thorough discussion of the constructed outranking models and of the best choice recommendation.

In this paper we illustrate some simple models for tackling uncertain criteria significance weights: uniform, triangular and beta laws. Applying the Central Limit Theorem, we are able to compute under these uncertainty models the actual likelihood of any pairwise \emph{at least as good as} situations. This operational result, by adequately handling potential veto and counter-veto situations, allows to enforce a given confidence level on the corresponding valued outranking situations. On a small illustrative best choice problem, we eventually show the pragmatic decision aid benefit one may expect from exploiting a confident versus a classic deterministic outranking digraph.

We propose an indirect approach for assessing robust criteria significance weights from global outranking statements that a decision maker may acknowledge in a Multiple Criteria Decision Aid process. Our approach takes advantage of the bipolar characteristic valuation of the global outranking and the eventual robustness of its associated Condorcet, i.e. median cut, crisp outranking relation. Numerical criteria significance weights are inferred with the help of a mixed integer linear programming model of which we present run tests results under different configurations and tunings.

In the context of Multiple Criteria Decision Aid, a decision-maker may be faced at any time with the task of analysing one or several sets of alternatives, irrespective of the decision he is about to make. As in this case the alternatives may express contrasting gains and losses on the criteria on which they are evaluated, and while the sets that are presented to the decision-maker may potentially be large, the task of analysing them becomes a difficult one. Therefore the need to reduce these sets to a more concise representation is very important. Classically, profiles that describe sets of alternatives may be found in the context of the sorting problem, however they are either given beforehand by the decision-maker or determined from a set of assignment examples. We would therefore like to extend such profiles, as well as propose new ones, in order to characterise any set of alternatives. For each of them, we present several approaches for extracting them, which we then compare with respect to their performance.

We introduce a bipolarly extended veto principle - a positive, as well as negative, large performance differences polarisation - which allows us to extend the definition of the classical outranking relation in such a way that the identity between its asymmetric part and its bipolar codual relation is preserved.

We generalize Kendall's rank correlation measure τ to bipolarly valued relations. Motivation for this work comes from the need to measure the level of ordinal approximation that is required when replacing a given bipolar outranking with a convenient weak ordering recommendation.

Complexity, credibility and change are three inevitable issues we face in modern decision-making problems. Integrating modern software requirements like rich user interaction, distributed architecture, agile application life-cycle development and full traceability may give the adequate answer to master these issues with our MCDA software.

We propose a meta-heuristic for clustering objects that are described on multiple incommensurable attributes of nominal, ordinal and/or cardinal type. Our approach makes use of an innovative bipolar-valued dual similarity-dissimilarity relation characterized by pairwise weighted majority margins of similar minus dissimilar attribute evaluations. The clustering is computed in two steps. First, an evolutionary algorithm searches for a suitable subset of maximal similarity cliques that will best serve as cluster cores. In a second step, we construct with a greedy heuristic, around these initial cluster cores, a corresponding final partition which best fits the given bipolar-valued similarity relation.

In this paper we introduce a bipolarly extended veto principle which allows us to extend the definition of the classic outranking relation in such a way that the identity between the asymmetric part and bipolar codual of the latter outranking relation is given.

Dans cet article, nous proposons une méthode indirecte d'élicitation robuste de l'importance des critères à partir d'informations préférentielles partielles exprimées par un décideur, dans un contexte de relations valuées bipolaires de surclassement. Nous montrons que la modélisation de telles informations par un modèle mathématique linéaire en variables mixtes suffit à estimer des poids numériques de signification des critères adéquats.

In this article we develop an indirect approach for assessing criteria significance weights from the robustness of the significance that a decision maker acknowledges for his pairwise outranking statements in a Multiple Criteria Decision Aiding process. The main result consists in showing that with the help of a mixed integer linear programming model this kind of a priori knowledge is sufficient for estimating adequate numerical significance weights.

The Decision Deck project is developing an open-source generic Multiple Criteria Decision Aid (MCDA) software platform composed of modular components. Its purpose is to provide effective tools for decision-aid consultants, for researchers in the field of MCDA, and for operations research teachers.

It is known that the number of maximal independent sets of the n-cycle graph C_n is given by 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 unlabelled (i.e., defined up to a rotation) maximal independent sets and the number of unlabelled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences.

We discuss the clustering of the set of criteria in a multicriteria decision analysis. Our approach is based on a generalisation of Kendall's rank correlation idea resulting in the definition of a bipolar ordinal correlation index. A factorial decomposition of this index allows to compute the principal inertia planes of the criteria correlations. The same ordinal correlation index, modelling a symmetric bipolar-valued similarity digraph, allows us to compute a criteria clustering from its maximal cliques.

Rubis is a new best choice decision method in the tradition of the Electre IS method that is available in the Decision-Deck software package. A brief description of it is given here, followed by a short illustrative application.

In this paper we discuss the clustering of the set of criteria in a multicriteria decision analysis. Our approach is based on a generalisation of Kendall's rank correlation index resulting in the definition of a bipolar ordinal correlation index. A factorial decomposition of this index allows to compute the principal inertia planes of the criteria correlations. The same ordinal correlation index, modelling a symmetric bipolar-valued similarity digraph, allows us to compute a criteria clustering from its maximal cliques.

In this article we show how the performances of alternatives and weights related to criteria can be determined from three different bipolar-valued outranking relations which are given beforehand. We furthermore detail how these results can be used in real-world decision problems in a disaggregation phase which helps to determine the different parameters linked to the representation of the decision maker’s preferences by an outranking relation.

The DECISION-DECK (D²) project's goal is an open source collaborative development of a generic Multiple Criteria Decision Analysis (MCDA) software platform composed of modular components. The genuine purpose is to provide effective tools for decision aid consultants, for researchers in the field of MCDA, as well as for OR teachers. The Distributed DECISION-DECK (D³) project's goal is to design and implement MCDA methods as Web Services (MCDA-WS). Operational requirements are the recommendation of XML standards for representing MCDA problems and solutions. In case of asynchronous MCDA-WS, as required for instance for the Rubis best choice decision method, a specific distributed D3 session server is needed. The D²-Rubis plugin is a D² resource for tackling the progressive best choice problem in the context of multiple criteria decision aiding. Its genuine purpose is to help a decision maker to determine a single best decision alternative.

The main concern of this article is to present the RUBIS method for tackling the choice problem in the context of multiple criteria decision aiding. Its genuine purpose is to help a decision maker to determine a single best decision alternative. Methodologically we focus on pairwise comparisons of these alternatives which lead to the concept of bipolar-valued outranking digraph. The work is centred around a set of five pragmatic principles which are required in the context of a progressive decision aiding methodology. Their thorough study and implementation in the outranking digraph lead us to define a choice recommendation as an extension of the classical digraph kernel concept.