Dealing with inconsistent judgments in multiple criteria sorting models.

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.Multicriteria decision aiding; Inconsistency analysis; Sorting problem;

Decision map for spatial decision making in urban planning

In this paper, we introduce the concept of decision map and illustrate the way this new concept can be used effectively to support participation in spatial decision making and in urban planning. First, we start by introducing our spatial decision process which is composed of five, non-necessary sequential, phases: problem identification and formulation, analysis, negotiation, concertation, and evaluation and choice. Negotiation and concertation are two main phases in spatial decision making but most available frameworks do not provide tools to support them effectively. The solution proposed here is based on the concept of decision map which is defined as an advanced version of conventional geographic maps which is enriched with preferential information and especially designed to clarify decision making. It looks like a set of homogenous spatial units; each one is characterised with a global, often ordinal, evaluation that represents an aggregation of several partial evaluations relative to different criteria. The decision map is also enriched with different spatial data exploration tools. The procedure of the construction of a decision map contains four main steps: definition of the problem (i.e. generation of criteria maps), generation of an intermediate map, inference of preferential parameters, and generation of a final decision map. The concept of decision map as defined here is a generic tool that may be applied in different domains. This paper focuses on the role of the decision map in supporting participation in spatial decision making and urban planning. Indeed, the decision map is an efficient communication tool in the sense that it permits to the different groups implied in the spatial decision process to ‘think visually’ and to communicate better between each other.ou

Using ELECTRE TRI outranking method to sort MOMILP nondominated solutions

Several interactive methods exist to identify nondominated solutions in a Multiple Objective Mixed Integer Linear Program. But what if the Decision Maker is also interested in sorting those solutions (assigning them to pre-established ordinal categories)? We propose an interactive "branch-and-bound like" technique to progressively build the nondominated set, combined with ELECTRE TRI method (Pessimistic procedure) to sort identified nondominated solutions. A disaggregation approach is considered in order to avoid direct definition of all ELECTRE TRI preference parameters. Weight-importance coefficients are inferred and category reference profiles are determined based on assignment examples provided by the Decision Maker. A computation tool was developed with a twofold purpose: support the Decision Maker involved in a decision process and provide a test bed for research purposes.http://www.sciencedirect.com/science/article/B6VCT-48GF3RT-B/1/55841cf788557c60dac156a4e7b1890

IRIS: a DSS for multiple criteria sorting problems

This paper presents Interactive Robustness analysis and parameters' Inference for multicriteria Sorting problems (IRIS), a Decision Support System (DSS) designed to sort actions (projects, candidates, alternatives, clients, etc.) described by their performances 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 that 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. Copyright © 2005 John Wiley & Sons, Ltd