| All publications sorted by year |
| 2009 |
| Abstract: | We consider the problem of assigning alternatives evaluated on several criteria into ordered categories C1, C2,..., Cp. This problem is known as the multi-criteria sorting problem and arises in many situations such as classifying countries into different risk levels based on economical and socio-political criteria, evaluating credit applications of bank customers. We are interested in sorting methods that are grounded on the construction of outranking relations. Among these, the Electre Tri method requires defining multidimensional profiles that represent the frontier separating consecutive categories Ch and Ch+1, and assigns an alternative to categories according to how it compares to each of the profiles. The explicit specification of the profiles of consecutive categories can be difficult for decision makers. We develop a new outranking based sorting method that does not require the explicit definition of profiles. We instead require the decision maker to assign a subset of reference alternatives to the categories. To assign the remaining alternatives, each such alternative is compared to reference alternatives, and assigned to categories accordingly |
| Abstract: | Planning as part of public sector decision-making situations is an activity of critical importance, with direct relevance for urban planners. The ramifications of such decisions generally have significant effect on peoples' lives. The current paper deals with the comparison between territorial maps in the context of districting problems with a strong socio-economic component. The theoretical problem involves the comparison of two partitions in a connected, undirected, and planar graph. In considering this problem, we introduce three new indices to compare territory partitions: compatibility, inclusion, and distance, all of which have importance for real-world planning situations. Numerical experiments of these indices were carried out for the communes network in Ile de France |
| 2008 |
| Abstract: | In this chapter we present a new interactive procedure for multiobjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from its approximation) is generated. In the second stage, the Decision Maker (DM) is asked to make pairwise comparisons of some solutions from the generated sample. Besides pairwise comparisons, the DM may compare selected pairs from the viewpoint of the intensity of preference, both comprehensively and with respect to a single criterion. This preference information is used to build a preference model composed of all general additive value functions compatible with the obtained information. The set of compatible value functions is then applied on the whole Pareto optimal set, which results in possible and necessary rankings of Pareto optimal solutions. These rankings are used to select a new sample of solutions, which is presented to the DM, and the procedure cycles until a satisfactory solution is selected from the sample or the DM comes to conclusion that there is no satisfactory solution for the current problem setting. Construction of the set of compatible value functions is done using ordinal regression methods called UTA-GMS and GRIP. These two methods generalize UTA-like methods and they are competitive to AHP and MACBETH methods. The interactive procedure will be illustrated through an example |
| Abstract: | Multicriteria analysis is a set of mathematical tools and methods allowing the comparison of di®erent alternatives according to many criteria, often con°icting, in order to guide the decision maker towards a judicious choice. Multicriteria methods are used in spatial context to evaluate and compare spatial decision alternatives, often modeled through constraint-based suitability analysis and represented by point, line, and polygon features or their combination, and evaluated on several space-related criteria, in order to select a restricted subset for implementation. Outranking methods, a family of multicriteria methods, may be useful in spatial decision problems, especially when ordinal evaluation criteria are implied. However, it is recognized that these methods, except those devoted to multicriteria classi¯cation problems, are subject to computational limitations with respect to the number of alternatives. This paper proposes a framework to facilitate the incorporation and use of outranking methods in geographical information systems (GIS). The framework is composed of two phases. The ¯rst phase allows producing a planar subdivision of the study area obtained by combining a set of criteria maps; each represents a particular vision of the decision problem. The result is a set of non-overlapping spatial units. The second phase allows constructing decision alternatives by combining the spatial units. Point, line and polygon feature-based decision alternatives are then constructed as an individual, a grouping of linearly adjacent or a grouping of contiguous spatial units. This permits to reduce considerably the number of alternatives, enabling the use of outranking methods. The framework is illustrated through the development of a prototype and through a step- by-step application to a corridor identi¯cation problem. The paper includes also a discussion of some conceptual and technical issues related to the framework |
| Abstract: | We present a new method, called UTA-GMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A^R \subseteq A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a,b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTA-GMS method is intended to be used interactively, with an increasing subset A^R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTA-GMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA-GMS software. Some extensions of the method are also presented |
| 2007 |
| Abstract: | We present a new method, called UTA-GMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A^R \subseteq A, called reference alternatives. The preference model built via ordinal regression is a set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete and negatively transitive relation. The UTA-GMS method is intended to be used interactively, with an increasing subset A^R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the all set of actions, UTA-GMS answers questions of robustness analysis. Moreover, the method can support the decision maker also when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA-GMS software. Some extensions of the method are also presented. |
| Abstract: | Fuzzy semantic model (FSM) is a data model that uses basic concepts of semantic modeling and supports handling fuzziness, uncertainty and imprecision of real-world at the attribute, entity and class levels. The paper presents the principles and constructs of the FSM. It proposes ways to de¯ne the membership functions within all the constructs of the FSM. In addition, it provides a proposal for specifying FSM schema and introduce a query language adapted to FSM-based databases |
| Abstract: | The objective of this paper is to propose a new algebra, called decision map algebra (DMA), especially devoted to multicriteria spatial modeling. DMA is a generic and context-independent modeling language inspired from map algebra and other similar languages. It supports the conventional geometric objects and cartographic maps and adds a rich set of new operands representing different spatial multicriteria concepts. Moreover, DMA supports different conventional map algebra-like operations and adds several new ones corresponding to different spatial multicriteria evaluation functions. The proposed algebra is the first step towards the development of a generic spatial multicriteria modeling language |
| Abstract: | This paper addresses the situation where a group wishes to cooperatively develop a common multicriteria evaluation model to sort actions (projects, candidates) into classes. It is based on an aggregation/disaggregation approach for the ELECTRE TRI method, implemented on the Decision Support System IRIS. We provide a methodology in which the group discusses how to sort some exemplary actions (possibly fictitious ones), instead of discussing what values the model parameters should take. This paper shows how IRIS may be used to help the group to iteratively reach an agreement on how to sort one or a few actions at a time, preserving the consistency of these sorting examples both at the individual level and at the collective level. The computation of information that may guide the discussion among the group members is also suggested. We provide an illustrative example and discuss some paths for future research motivated by this work. |
| Abstract: | In decision analysis, difficulties of obtaining complete information about model parameters make it advisable to seek robust solutions that perform reasonably well across the full range of feasible parameter values. In this paper, we develop the Robust Portfolio Modeling (RPM) methodology which extends Preference Programming methods into portfolio problems where a subset of project proposals are funded in view of multiple evaluation criteria. We also develop an algorithm for computing all non-dominated portfolios, subject to incomplete information about criterion weights and project-specific performance levels. Based on these portfolios, we propose a project-level index to convey (i) which projects are robust choices (in the sense that they would be recommended even if further information were to be obtained) and (ii) how continued activities in preference elicitation should be focused. The RPM methodology is illustrated with an application using real data on road pavement projects. |
| Abstract: | Districting problems are of high importance in many different fields. Multiple criteria models seem a more adequate representation of districting problems in real-world situations. Real-life decision situations are by their very nature multidimensional. This paper deals with the problem of partitioning a territory into ``homogeneous'' zones. Each zone is composed of a set of elementary territorial units. A district map is formed by partitioning the set of elementary units into connected zones without inclusions. When multiple criteria are considered, the problem of enumerating all the efficient solutions for such a model is known as being NP-hard, which is why we decided to avoid using exact methods to solve large-size instances. In this paper, we propose a new method to approximate the Pareto front based on an evolutionary algorithm with local search. The algorithm presents a new solution representation and the \emph{crossover/mutation} operators. Its main features are the following: it deals with multiple criteria; it allows to solve large-size instances in a reasonable CPU time and generates high quality solutions. The algorithm was applied to a real-world problem, that of the Paris region public transportation. Results will be used for a discussion about the reform of its current pricing system |
| 2006 |
| Abstract: | When considering Electre’s valued outranking relations, aggregation/disaggregation methodologies have difficulties in taking discordance (veto) into account. We present a partial inference procedure to compute the value of the veto-related parameters that best restore a set of outranking statements (i.e., examples that an Electre model should restore) provided by a decision maker, given fixed values for the remaining parameters of the model. This paper complements previous work on the inference of other preference-related parameters (weights, cutting level, category limits, …), advancing toward an integrated framework of inference problems in Electre III and Tri methods. We propose mathematical programs to infer veto-related parameters, first considering only one criterion, then all criteria simultaneously, using the original version of Electre outranking relation and two variants. This paper shows that these inference procedures lead to linear programming, 0–1 linear programming, or separable programming problems, depending on the case. |
| Abstract: | Sorting models consist in assigning alternatives evaluated on several criteria to ordered categories. To implement such models it is necessary to set the values of the preference parameters used in the model. Rather than fixing the values of these parameters directly, a usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which (s)he specifies a required category. However, assignment examples provided by DMs can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we extend algorithms from Mousseau et al. 2003 that calculate different ways to remove assignment examples so that the information can be represented in the sorting model. The extension concerns the possibility to relax (rather than to delete) assignment examples. These algorithms incorporate information about the confidence attached to each assignment example, hence providing inconsistency resolutions that the DMs are most likely to accept. |
| Abstract: | "" |
| 2005 |
| Abstract: | This paper introduces the concept of decision map and illustrates the way this new concept can be used in spatial decision making and in urban planning. The decision map is defined as an advanced version of conventional geographic maps which is enriched with preferential information and especially destined to "visual" spatial decision making. The concept of decision map as defined here is a generic tool that may be applied in different domains. This paper focuses on its role in supporting participation in spatial decision making and urban planning. |
| Abstract: | We present a new method (called UTAGMS) for multiple criteria ranking using strongly and weakly established weak preference relations which result from an ordinal regression. The preference information supplied by the decision maker is a set of pairwise comparisons of reference alternatives. The preference model built via ordinal regression is a set of general additive value functions. The method provides two final rankings: a strong ranking identifying ''sure'' preference statements, and a weak ranking identifying ''possible'' preference statements. In order to build these two rankings, the method takes into account all value functions compatible with the preference information. The UTAGMS method is intended to be used interactively, with progressive statement of pairwise comparisons. Moreover, the method can support the decision maker also when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTAGMS software. Some extensions of the method are also presented |
| 2004 |
| Abstract: | In ELECTRE methods, the construction of an outranking relation amounts at validating or invalidating, for any pair of alternatives (a,b), the assertion "a is at least as good as b". This comparison is grounded on the evaluation vectors of both alternatives, and on additional information concerning the decision maker's preferences, accounting for two conditions: concordance and non-discordance. In decision processes using these methods, the analyst should interact with the decision maker in order to elicit values for preferential parameters. This can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the decision maker. Inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an "error function". Although disaggregation approaches have been largely used in additive models, only few advances have been made towards a disaggregation approach for outranking methods. Indeed, outranking methods may lead to computationally difficult inference problems. In this paper we are concerned with a slight adaptation of the valued outranking relation used in the ELECTRE III and ELECTRE TRI. Such modification is shown to preserve the original discordance concept. We show that the modified outranking relation makes it easier to solve inference programs. |
| Abstract: | Some decision problems can be formulated as sorting models which consist in assigning alternatives evaluated on several criteria to ordered categories. The implementation of a multiple criteria sorting model requires to set the values of the preference parameters used in the model. Rather than fixing directly the values of these parameters, an usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which he/she specifies a required category or interval of acceptable categories. However, the judgments expressed by DMs through assignment examples can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we propose algorithms that calculate different ways to modify the set of assignment examples so that the information can be represented in the sorting model. The modifications considered are either the removal of examples or the relaxation of existing assignments. These algorithms incorporate information about the confidence attached by the DMs to each assignment example. These algorithms aim at finding and ranking the solutions to solve inconsistency that the DMs are most likely to accept. |
| Abstract: | Some decision problems can be formulated as sorting models which consist in assigning alternatives evaluated on several criteria to ordered categories. The implementation of a multiple criteria sorting model requires to set the values of the preference parameters used in the model. Rather than fixing directly the values of these parameters, an usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which he/she specifies a required category or interval of acceptable categories. \\ However, the judgments expressed by DMs through assignment examples can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we propose algorithms that calculate different ways to modify the set of assignment examples so that the information can be represented in the sorting model. The modifications considered are either the removal of examples or the relaxation of existing assignments. These algorithms incorporate information about the confidence attached by the DMs to each assignment example. These algorithms aim at finding and ranking the solutions to solve inconsistency that the DMs are most likely to accept. |
| 2003 |
| Abstract: | This paper presents IRIS (Interactive Robustness analysis and parameters' Inference for multicriteria Sorting problems), a Decision Support System (DSS) designed to sort actions (projects, candidates, alternatives, clients, ...) described by their performance on multiple criteria into an ordered set of categories defined a priori. It is based on the ELECTRE TRI sorting method, but does not require the Decision Maker (DM) to indicate precise values for all of the method's parameters. More realistically, the software expects the DM to indicate some constraints these parameters should respect, including sorting examples that the program should reproduce. If the constraints indicated by the DM do not contradict each other (i.e. form a consistent system), then IRIS infers a combination of parameter values that reproduces all the sorting examples, indicating also the range of possible assignments of actions to categories that would be possible without violating any of the stated constraints. If the constraints are contradictory (i.e. form an inconsistent system), then IRIS suggests a combination of parameter values that minimizes an error function and identifies alternative ways to restore the system's consistency by removing some constraints. |
| Abstract: | A successful application of the interactive multiobjective optimization method NIMBUS to a design problem in papermaking technology is described. Namely, an optimal shape design problem related to the paper machine headbox is studied. First, the NIMBUS method, the numerical headbox model, and the associated multiobjective optimization problem are described. Then, the results of numerical experiments are presented |
| Abstract: | In this paper, sufficient conditions for superstrict minima of order m to nondifferentiable multiobjective optimization problems with an arbitrary feasible set are provided. These conditions are expressed through the Studniarski derivative of higher order. If the objective function is Hadamard differentiable, a characterization for strict minimality of order 1 (which coincides with superstrict minimality in this case) is obtained |
| Abstract: | "We consider a framework where Decision Makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the model's parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using 0-1 programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method." |
| Abstract: | We provide an answer to an open problem concerning the representation of preferences by intervals. Given a finite set of elements and three relations on this set (indifference, weak preference and strict preference), necessary and sufficient conditions are provided for representing the elements of the set by intervals in such a way that (1) two elements are indifferent when the interval associated to one of them is included in the interval associated to the other; (2) an element is weakly preferred to another when the interval of the first is "more to the right" than the interval of the other, but the two intervals have a non-empty intersection; (3) an element is strictly preferred to another when the interval of the first is "more to the right" than the interval of the other and their intersection is empty |
| Abstract: | In this article, we propose a new soft constraint called preference constraint, squaring well with the decision theory concept of preference binary relation. We show how to use it for designing complex hierarchical preference information based on preference binary relations for combinatorial problems. Finally, preference-based constraint systems are defined and associated best quality choice problems are introduced. This new model offers greater flexibility to represent and make complex decisions with computers |
| Abstract: | "We consider the Multiple Criteria Sorting Problem, that aims at assigning each alternative in a finite set $A$ to one of the predefined categories. We propose a new concept of category size that refers to the proportion by which an evaluation vector corresponding to a realistic alternative is assigned to the category. Sorting problems usually refer to absolute evaluation (the assignment of an alternative does not depend on the others), as opposed to ranking and choice problems in which the very purpose is to compare alternatives against each other. Considering constraints concerning category size lead to define a Constrained Sorting Problem which refers both to absolute and relative evaluation. After identifying decision situations in which category size is useful for modelling purposes, this paper defines the concept of category size and proposes a way to compute the size of categories, even when the set of alternatives and/or the preference information is/are imprecisely known. We show how this notion can be used in a preference elicitation process. Finally, in order to illustrate the use of this concept, we propose a procedure to infer the values for preference parameters that accounts for specifications (provided by the DM) about the size of categories, in the context of the UTADIS sorting model." |
| 2002 |
| Abstract: | "ELECTRE TRI is a well-known method to assign a set of alternatives to a set of predefined categories, considering multiple criteria. Using this method requires setting many parameters, which is often a difficult task. We consider the case where the Decision Makers (DMs) in the decision process are not sure of which values should each parameter take, which may result from uncertain, imprecise or inaccurately determined information, as well as from a lack of consensus among them. This paper discusses the synergy between two approaches developed independently to deal with this difficulty. Both approaches avoid asking for precise values for the parameters. Rather, they proceed to solve the problem in a way that requires from the DMs much less effort. The first approach infers the value of parameters from assignment examples provided by the DMs. Each assignment example originates mathematical constraints to which the parameter values should satisfy. The second approach considers a set of constraints on the parameter values reflecting the imprecise information that the DMs are able to provide. Then, it computes the best and worst categories for each alternative compatible with constraints. This paper proposes a new approach integrating the elicitation phase with robustness analysis, to exploit the synergy between them. It is an interactive approach, where the insight obtained during robustness analyses guides the DMs during the elicitation phase." |
| Abstract: | "Given a finite set of alternatives, the sorting (or assignment) problem consists in the assignment of each alternative to one of the predefined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of preferential parameters (importance coefficients, thresholds, profiles, etc.) in order to construct the decision-maker's (DM) preference model. A direct elicitation of these parameters being sometimes difficult, Mousseau and Slowinski proposed an interactive aggregation-disaggregation approach that infer ELECTRE TRI parameters indirectly from holistic information, i.e. assignment examples. In this approach, the determination of ELECTRE TRI parameters that best restore the assignment examples is formulated through a non-linear optimization program. Also in this direction, Mousseau et al. considered the subproblem of the determination of the importance coefficients only (the thresholds and category limits being fixed). This subproblem leads to solve a linear program (rather that non-linear in the global inference model). We pursue the idea of partial inference model by considering the complementary subproblem which determines the category limits (the importance coefficients being fixed). With some simplification, it also leads to solve a linear program. Together with the result of Mousseau et al., we have a couple of complementary models which can be combined in an interactive approach inferring the parameters of an ELECTRE TRI model from assignment examples. In each interaction, the DM can revise his/her assignment examples, to give additional information and to choose which parameters to fix before the optimization phase restarts." |
| Abstract: | "Les méthodes d'aide multicritère à la décision laissent une large gamme de modalités d'application notamment lorsque la décision implique plusieurs acteurs. La construction collective des modèles d'aide à la décision multicritère a trait à la manière de mener avec les décideurs la phase de structuration, d'élaboration de l'ensemble des actions potentielles, de construction d'une famille (ou une hiérarchie) de critères, d'élicitation les préférences. Le mode d'implication des acteurs dans la construction collective de modèle muticritère est étudié dans cet article. L'analyse s'appuie sur une application réelle, dans le domaine de la tarification des transport publics." |
| Abstract: | "When considering Electre's valued outranking relations, aggregation/disaggregation methodologies have difficulties in taking discordance (veto) into account. We present a partial inference procedure to compute the value of the veto-related parameters that best restore a set of outranking statements, provided by a decision maker ({\it i.e.}, examples that an Electre model should restore).\\ This paper complements previous work on the inference of other preference-related parameters (weights, cutting level, category limits, ...), advancing toward an integrated approach to inference problems in Electre III and Tri methods. We propose mathematical programs to infer veto-related parameters, first considering only one criterion, then all criteria simultaneously, using the original version of Electre outranking relation and two variants. Depending on the case, these inference procedures lead to linear programming, 0-1 linear programming, or separable programming problems.\\ The partial inference programs are considered as problems to be solved several times in an interactive process, where the DM(s)\ continuously revise the information they provide as they learn from the results" |
| Abstract: | When considering Electre's valued outranking relations, aggregation/disaggregation methodologies have difficulties in taking discordance (veto) into account. We present a partial inference procedure to compute the value of the veto-related parameters that best restore a set of outranking statements, provided by a decision maker ( i.e., examples that an Electre model should restore). This paper complements previous work on the inference of other preference-related parameters (weights, cutting level, category limits, ...), advancing toward an integrated approach to inference problems in Electre III and Tri methods. We propose mathematical programs to infer veto-related parameters, first considering only one criterion, then all criteria simultaneously, using the original version of Electre outranking relation and two variants. Depending on the case, these inference procedures lead to linear programming, 0-1 linear programming, or separable programming problems. The partial inference programs are considered as problems to be solved several times in an interactive process, where decision makers continuously revise the information they provide as they learn from the results. |
| 2001 |
| Abstract: | "Observation of social and economic trends has led the Syndicat des Transports Parisiens (STP, the Paris transport authority) to re-examine the ticket price system as it is today. Reform of this system will involve a great many stakeholders in the transport world, whose interests are not necessarily the same; they must participate in this project so that a future ticket pricing structure will be acceptable to all. Therefore all those involved must be able to take part in the study which will precede the decisions. With this in mind, the STP has called for a methodological study which will allow the impact of ticket price changes based on zoning to be evaluated. The main lines of research concern three phases: {\bf 1} Definition and evaluation of zoning choices in the Ile de France, {\bf 2} Quality analysis of potential offer and demand in the zones thus selected, {\bf 3} Evaluation and comparison of the various ticket pricing hypotheses. This methodology will take the form of software which will be the basis for analysis and dialogue between the stakeholders involved in ticket price changes. This software must allow first, input, evaluation, modification and comparison of zoning choices, and second, the transport offer and the potential demand for each zoning choice to be analysed in order to design and evaluate the impact of a ticket pricing scenario applied to the zoning choice on the basis of hypothetical traffic flow evolution." |
| Abstract: | "Given a finite set of alternatives $A$, the sorting (or assignment) problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of preferential parameters (weights, thresholds, category limits,...) in order to construct a preference model with which the Decision Maker (DM) accept as a working hypothesis in the decision aid study. A direct elicitation of these parameters requiring a high cognitive effort from the DM, Mousseau, Slowinski 98 proposed an interactive aggregation-disaggregation approach that infer ELECTRE TRI parameters indirectly from hollistic information, {\it i.e.}, assignment examples. In this approach, the determination of ELECTRE TRI parameters that best restitute the assignment examples is formulated through a non-linear optimization program. In this paper, we consider the subproblem of the determination of the weights only (the thresholds and category limits being fixed). This subproblem leads to solve a linear program (rather than non-linear in the global inference model). Numerical experiments were conducted so as to check the abilities of this disagregation tool. Results showed that this tool is able to infer weights that restitutes in a stable way the assignment examples and that it is able to identify {\it inconsistencies} in the assignment examples." |
| Abstract: | "We consider a framework where Decision Makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the model's parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using 0-1 programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method." |
| Abstract: | "In ELECTRE methods, the construction of an outranking relation $S$ amounts at validating or invalidating, for any pair of alternatives $(a,b) \in A$, an assertion $aSb$. This comparison is grounded on the evaluation vectors of both alternatives, and on additional information concerning the DM's preferences, accounting for two conditions: concordance and non-discordance. In decision processes using these methods, the analyst should interact with DM(s) in order to elicit values for preferential parameters. This can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the DM(s). Inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an ``error function''. Although disaggregation approaches have been largely used in additive models, only few advances have been made towards a disaggregation approach for ELECTRE type methods. This probably reflects the ``optimization unfriendly'' character of the most recent ELECTRE methods.\\ In this paper we are concerned with a slight adaptation of the valued outranking relation used in the ELECTRE III and ELECTRE TRI that preserves the original ideas and is more optimization-friendly for parameter inference programs. Such modification is shown to preserve the original discordance concept. We show that the modified outranking relation makes it easier to solve inference programs." |
| Abstract: | "In ELECTRE methods, the construction of an outranking relation $S$ amounts at validating or invalidating, for any pair of alternatives $(a,b) \in A$, an assertion $aSb$. This comparison is grounded on the evaluation vectors of both alternatives, and on additional information concerning the DM's preferences, accounting for two conditions: concordance and non-discordance. In decision processes using these methods, the analyst should interact with DM(s) in order to elicit values for preferential parameters. This can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the DM(s). Inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an ``error function''. Although disaggregation approaches have been largely used in additive models, only few advances have been made towards a disaggregation approach for ELECTRE type methods. This probably reflects the ``optimization unfriendly'' character of the most recent ELECTRE methods.\\ In this paper we are concerned with a slight adaptation of the valued outranking relation used in the ELECTRE III and ELECTRE TRI that preserves the original ideas and is more optimization-friendly for parameter inference programs. Such modification is shown to preserve the original discordance concept. We show that the modified outranking relation makes it easier to solve inference programs." |
| 2000 |
| Abstract: | "Des constats socio-économiques ont amené le Syndicat des Transports Parisiens (STP) à repenser le système de tarification des transports publics en vigueur actuellement. Une telle réforme tarifaire implique un grand nombre d'acteurs du monde du transport dont les intérêts peuvent diverger ; ceux-ci doivent participer à ce projet en vue de concevoir une future structure tarifaire acceptable par tous. Ceci nécessite que l'ensemble des acteurs concernés puisse prendre part aux réflexions qui précédent les décisions. C'est dans ce cadre que le STP a sollicité un travail méthodologique visant à permettre d'évaluer l'impact d'une évolution tarifaire reposant sur le découpage d'un territoire en zones. Les grandes lignes de la recherche s'organisent principalement autour de trois phases : {\bf 1} la définition et l'évaluation de zonages partitionnant l'Ile-de-France en zones, {\bf 2} l'analyse du niveau qualitatif de l'offre et de demande potentielle dans les zonages préalablement définis, {\bf 3} l'évaluation et la comparaison de différentes hypothèses de tarification. Cette méthodologie se concrétise par le développement d'un logiciel qui va servir de base de réflexion et de communication entre acteurs impliqués dans un processus d'évolution tarifaire. Ce logiciel doit permet d'une part de saisir, d'évaluer, de modifier et de comparer des zonages puis, d'autre part, d'analyser l'offre de transport et la demande potentielle des zones d'un zonage défini en vue de concevoir et d'évaluer l'impact d'un scénario de tarification appliqué à ce zonage sur la base d'hypothèse d'évolution de trafic." |
| Abstract: | "Multiple Criteria Sorting Problem consists in assigning a set of alternatives $A=\lbrace a_1, a_2, ..., a_l \rbrace$ evaluated on $n$ criteria $g_1, g_2, ..., g_n$ to one of the categories which are pre-defined by some norms corresponding to vectors of scores on particular criteria, called profiles, either separating the categories or playing the role of central reference points in the categories. The assignment of an alternative $a_k$ to a specific category results from a comparison of its evaluation on all criteria with the profiles defining the categories. This paper presents a new implementation of an existing method called ELECTRE TRI. It integrates specific functionalities supporting the Decision Maker (DM) in the preference elicitation process. These functionalities grouped in ELECTRE TRI Assistant aim at reducing the cognitive effort required from the DM in the phase of calibration of the preference model. The main characteristic feature of ELECTRE TRI Assistant is the inference of the ELECTRE TRI preferential parameters from assignment examples supplied by the DM. The software is presented through an illustrative example." |
| Abstract: | "This paper presents a new approach to support evaluating a set of objects on a hierarchy of qualitative criteria. Evaluating an object on a node with respect to its evaluations on the sub-nodes is formulated as a multicriteria classification problem where the levels of the node's scale correspond to the ordered classes. Different multicriteria classification methods can be used. Selection of the adequate method(s) depends on many criteria or attributes involving context factors, characteristics of the methods and performances of the models." |
| Abstract: | "We consider a framework where Decision Makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the model's parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using 0-1 programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method." |
| Abstract: | "ELECTRE TRI is a well-known method to assign a set of alternatives to a set of predefined categories, considering multiple criteria. Using this method requires setting many parameters, which is often a difficult task. We consider the case where the Decision Makers (DMs) in the decision process are not sure of which values should each parameter take, which may result from uncertain, imprecise or inaccurately determined information, as well as from a lack of consensus among them. This paper discusses the synergy between two approaches developed independently to deal with this difficulty. Both approaches avoid asking for precise values for the parameters. Rather, they proceed to solve the problem in a way that requires from the DMs much less effort. The first approach infers the value of parameters from assignment examples provided by the DMs. Each assignment example originates mathematical constraints to which the parameter values should satisfy. The second approach considers a set of constraints on the parameter values reflecting the imprecise information that the DMs are able to provide. Then, it computes the best and worst categories for each alternative compatible with constraints. This paper proposes a new approach integrating the elicitation phase with robustness analysis, to exploit the synergy between them. It is an interactive approach, where the insight obtained during robustness analyses guides the DMs during the elicitation phase." |
| Abstract: | "Given a finite set of alternatives, the sorting (or assignment) problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of preferential parameters (importance coefficients, thresholds, profiles,...) in order to construct the DM's preference model. A direct elicitation of these parameters being sometimes difficult, \cite{mous2jogo98} proposed an interactive aggregation-disaggregation approach that infer ELECTRE TRI parameters indirectly from holistic information, i.e., assignment examples. In this approach, the determination of ELECTRE TRI parameters that best restitute the assignment examples is formulated through a non-linear optimization program. Also in this direction, \cite{mouss3ejor01} considered the subproblem of the determination of the importance coefficients only (the thresholds and category limits being fixed). This subproblem leads to solve a linear program (rather that non-linear in the global inference model). \\ We pursue the idea of partial inference model by considering the complementary subproblem which determines the category limits (the importance coefficients being fixed). With some simplification, it also leads to solve a linear program. Together with the result of \cite{mouss3ejor01}, we have a couple of complementary models which can be combined in an interactive approach inferring the parameters of an ELECTRE TRI model from assignment examples. In each interaction, the DM can revise his/her assignment examples, to give additional information and to choose which parameters to fix before the optimization phase restarts." |
| 1999 |
| Abstract: | "Multiple criteria decision aiding methodologies rely on basic principles concerning the consistency of decision maker's (DM's) preferences. Among these principles, the Third Alternative Invariance (TAI) principle states that elicited preferences on two alternatives should not be affected by the presence or availability of a third alternative. Empirical statements on cognitive limitations of decision makers tends to contradict this principle. Our work aims at analysing the behavior of DMs when answering binary and ternary choice questions. Results show a violation of the TAI principle. Such results may be explained by a shift in the reference points considered by decision makers in the binary and ternary choice questions. Implications for preference elicitation techniques in multiple criteria decision aid are discussed." |
| Abstract: | "This paper presents a new approach to support evaluating a set of objects on a hierarchy of qualitative criteria. Evaluating an object on a node with respect to its evaluations on the sub-nodes is formulated as a multicriteria classification problem where the levels of the node's scale correspond to the ordered classes. Different multicriteria classification methods can be used. Selection of the adequate method(s) depends on many criteria or attributes involving context factors, characteristics of the methods and performances of the models." |
| Abstract: | "Multiple Criteria Sorting Problem consists in assigning a set of $A=\{a_1, a_2, ..., a_l\} evaluated on $n$ criteria $g_1, g_2, ..., g_n to one of the categories which are pre-defined by some norms corresponding to vectors of scores on particular criteria, called profiles, either separating the categories or playing the role of central reference point in the categories. The assignment of an alternative ak to a specific category follows from a comparison of its evaluation on all criteria with the profiles defining the categories. This document presents a new implementation of an existing method called ELECTRE TRI. It integrates specific functionalities supporting the Decision Maker (DM) in the preference elicitation process. These functionalities grouped in ELECTRE TRI Assistant aim at reducing the cognitive effort required from the DM in the phase of calibration of the model. The main characteristic feature of ELECTRE TRI Assistant is the inference of the ELECTRE TRI preferential parameters from assignment examples supplied by the DM. The software is presented through an illustrative example." |
| 1998 |
| Abstract: | "Given a finite set of alternatives, the sorting problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of parameters (weights, thresholds, category limits,...) in order to construct the DM's preference model. A direct elicitation of these parameters being rather difficult, we proceed to solve this problem in a way that requires from the DM much less cognitive effort. We elicit these parameters indirectly using hollistic information given by the DM through assignment examples. We propose an interactive approach that infers the parameters of an ELECTRE TRI model from assignment examples. The determination of an ELECTRE TRI model that best restitutes the assignement examples is formulated through an optimization problem. The interactive aspect of this approach lies in the possibility given to the DM to revise his/her assignment examples and/or to give additional information before the optimization phase restarts." |
| 1997 |
| Abstract: | The São Paulo State Watershed Program (PEMH) was drawn with multiple objectives. Minimization of runoff caused problems was ranked higher among those objectives. One of PEMH’s tools is the Sustainable Planning of Soil Use (PUSS) based on potential runoff effects, soil fertility, machinery use, and soil drainage to recommend appropriate conservation practices and more suitable activities to the farm system. Important dimensions that must be considered in implementing the PEMH are farmer objectives and the corresponding farm restrictions. Lexicographic optimization was used to plan the mix of activities for each farm. These objectives were: minimization of runoff effects, pesticide use, seasonal income variability, and seasonal demand for labor; and maximization of farm gross margin, basic staple production, and resident labor use. The optimization process pointed to activities that affected the farm system in different forms. When maximization of farm gross margin was not the first priority the optimization process pointed to plans that were not economically sustainable. Therefore, the lexicographic goal programming approach should be used carefully for farm planning when implementing The PEMH |
| Abstract: | "This paper empirically studies the influence a questioning mode can have on elicited preferences. The preference structure of decision makers is elicited using two different questioning modes: choice and matching. The results show a strong failure of procedure invariance. The impact on preference modelling and on importance parameter elicitation techniques is discussed." |
| Abstract: | "Given a finite set of alternatives $A$, the sorting (or assignment) problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of preferential parameters (weights, thresholds, category limits,...) in order to construct a preference model with which the Decision Maker (DM) accept as a working hypothesis in the decision aid study. A direct elicitation of these parameters requiring a high cognitive effort from the DM, \cite{mous2jogo98} proposed an interactive aggregation-disaggregation approach that infer ELECTRE TRI parameters indirectly from hollistic information, i.e., assignment examples. In this approach, the determination of ELECTRE TRI parameters that best restitute the assignment examples is formulated through a non-linear optimization program. In this paper, we consider the subproblem of the determination of the weights only (the thresholds and category limits being fixed). This subproblem leads to solve a linear program (rather than non-linear in the global inference model). Numerical experiments were conducted so as to check the abilities of this disagregation tool. Results showed that this tool is able to infer weights that restitutes in a stable way the assignment examples and that it is able to identify ``inconsistencies'' in the assignment examples." |
| 1996 |
| Abstract: | "Multiple-criteria decision aid almost always requires the use of weights, importance coefficients or even a hierarchy of criteria, veto thresholds, etc. These are importance parameters that are used to differentiate the role devoted to each criterion in the construction of comprehensive preferences. Many researchers have studied the problem of how to assign values to such parameters, but few of them have tried to analyse in detail what underlies the notion of importance of criteria and to give a clear formal definition of it. In this paper our purpose is to define a theoretical framework so as to analyse the notion of the importance of criteria under very general conditions. Within this framework it clearly appears that the importance of criteria is taken into account in very different ways in various aggregation procedures. This framework also allows us to shed new light on fundamental questions such as: Under what conditions is it possible to state that one criterion is more important than another? Are importance parameters of the various aggregation procedures dependent on or independent of the encoding of criteria? What are the links between the two concepts of the importance of criteria and the compensatoriness of preferences? This theoretical framework seems to us sufficiently general to ground further research in order to define theoretically valid elicitation methods for importance parameters." |
| Abstract: | "Given a finite set of alternatives, the sorting problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of parameters (weights, thresholds, category limits,...) in order to construct the DM's preference model. A direct elicitation of these parameters being rather difficult, we proceed to solve this problem in a way that requires from the DM much less cognitive effort. We elicit these parameters indirectly using hollistic information given by the DM through assignment examples. We propose an interactive approach that infers the parameters of an ELECTRE TRI model from assignment examples. The determination of an ELECTRE TRI model that best restitutes the assignement examples is formulated through an optimization problem. The interactive aspect of this approach lies in the possibility given to the DM to revise his/her assignment examples and/or to give additional information before the optimization phase restarts." |
| 1995 |
| Abstract: | "The notion of Relative Importance of Criteria (RIC) is central in the domain of Multiple Criteria Decision Aid (MCDA). It aims at differentiating the role of each criterion in the construction of comprehensive preferences, thus allowing to discriminate among pareto-optimal alternatives. In most aggregation procedures, this notion takes the form of importance parameters. The acquisition of information concerning the RIC may be supported by Elicitation Techniques for Importance Parameters (ETIP). The design of such techniques should account for both the meaning that each aggregation confers on its parameters and the decision makers' (DMs) understanding of the notion of RIC. More precisely, ETIPs should be able to provide a good fit between the way the analyst uses the DM's assertions in the model and the information that he/she expresses through his/her statements. In this paper, we present an ETIP adapted to the ELECTRE methods that proceeds by means of pairwise comparisons of fictitious alternatives. Implemented in a software program called DIVAPIME, this ETIP supports the elicitation of variation intervals for the ELECTRE methods' preferential parameters." |
| 1994 |
| 1993 |
| Abstract: | "Ce travail s'inscrit dans un courant de recherche qui vise à modéliser les situations décisionnelles en prenant en compte plusieurs objectifs ou points de vue : l'aide multi-critère à la décision. Dans ce champ de recherche, la notion d'importance relative des critères (IRC) est centrale puisqu'elle vise à distinguer le rôle de chaque critère dans l'élaboration des préférences globales, permettant ainsi de discriminer entre les actions pareto-optimales. Dans la plupart des procédures d'agrégation, cette notion prend la forme de paramètres d'importance ; notre thèse a pour but de développer des méthodes d'évaluation de ces paramètres. Pour justifier la conception de telles méthodes, des travaux à la fois théoriques et expérimentaux ont été nécessaires. D'un point de vue théorique, la nature et la signification des paramètres d'importance sont propres à chaque méthode d'agrégation : les valeurs qui leur sont attribuées ne prennent un sens qu'en relation avec une règle d'agrégation. Après avoir introduit une définition formelle de l'IRC, nous montrons comment cette formalisation éclaire sous un jour nouveau certaines difficultés théoriques liées à l'évaluation de l'IRC. Par ailleurs, les expériences réalisées permettent de préciser la perception qu'ont les décideurs de la notion d'IRC ainsi que les questions s'y rapportant. Nous cherchons alors à déterminer comment recueillir, auprès d'un décideur, une information sur l'importance relative des critères qui soit à la fois valide d'un point de vue théorique et pertinente d'un point de vue comportementaliste. Ceci nous conduit à énoncer quelques caractéristiques que toute méthode d'évaluation des paramètres d'importance doit respecter. Nous présentons enfin une méthode d'acquisition de l'information préférentielle requise dans les méthodes ELECTRE. Cette méthode est implémentée et les fonctionnalités du logiciel sont illustrées à travers un exemple concret." |
| 1992 |
| Abstract: | "La notion d'importance relative des critères est centrale en aide multicritère à la décision. Elle est utilisée dans une très grande majorité de méthodes à travers des paramètres d'importance qui visent à distinguer le rôle de chaque critère dans l'élaboration des préférences globales. Ce document recense une grande partie des articles qui, à notre connaissance, sont parus dans le domaine et donne une analyse critique de cette littérature. De plus, une classification à deux niveaux est proposée. Le premier niveau permet de regrouper en catégories les travaux de même nature. Le second niveau est transversal au premier et permet de situer rapidement (grâce à des indicateurs sémantiques) l'orientation globale de chaque publication." |
| Abstract: | "Multiple-criteria decision aid almost always requires the use of weights, importance coefficients or even a hierarchy of criteria, veto thresholds, etc. These are importance parameters that are used to differentiate the role devoted to each criterion in the construction of comprehensive preferences. Many researchers have studied the problem of how to assign values to such parameters, but few of them have tried to analyse in detail what underlies the notion of importance of criteria and to give a clear formal definition of it. In this paper our purpose is to define a theoretical framework so as to analyse the notion of the importance of criteria under very general conditions. Within this framework it clearly appears that the importance of criteria is taken into account in very different ways in various aggregation procedures. This framework also allows us to shed new light on fundamental questions such as: Under what conditions is it possible to state that one criterion is more important than another? Are importance parameters of the various aggregation procedures dependent on or independent of the encoding of criteria? What are the links between the two concepts of the importance of criteria and the compensatoriness of preferences? This theoretical framework seems to us sufficiently general to ground further research in order to define theoretically valid elicitation methods for importance parameters." |
| Abstract: | "This paper describes an experimental work about relative importance of criteria in Multiple Criteria Decision Aid. Empirical results show that intuitive weight and decisivity of criteria change when the set of potential alternatives is modified. Impacts on preference modelling and importance parameter elicitation methods are discussed. " |
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