Using assignment examples to infer weights for ELECTRE TRI method: Some experimental results

TLDR: Results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it was able to identify “inconsistencies” in the assignmentExamples.

About: This article is published in European Journal of Operational Research.The article was published on 2001-04-16 and is currently open access. It has received 230 citations till now. The article focuses on the topics: ELECTRE.

Figures

Fig. 1. General scheme of the inference procedure.

Table 6 err100opt i : number of incorrect reassignments

Table 5 a100opt i : ability of w to reassign alternatives

Table 4 Identi®cation of ``errors''

Table 1 Type of errors introduced in the sets

Fig. 2. De®nition of categories using limit pro®les.

Frequently asked questions

Q1. What have the authors contributed in "Using assignment examples to infer weights for electre tri method: some experimental results" ?

In this paper, the authors 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 which the decision maker ( DM ) accepts as a working hypothesis in the decision aid study. In this paper, the authors consider the subproblem of the determination of the weights only ( the thresholds and category limits being ®xed ). 

Q2. What is the way to infer a weight vector wopt?

In order to infer in a reliable way a weight vector wopt, the optimization procedure requires information as input, i.e., on the set of assignment examples. 

Q3. What is the purpose of the inference phase?

The inference phase (formalized by the mathematical program) is not only a simply adjustment process, but is intended to be integrated into an interactive aggregation disaggregation process (see Section 2). 

Q4. What is the general form of the considered objective function z to be maximized?

The general form of the considered objective function z to be maximized isz min k : ak2Afxk; ykg e Xk : ak2A xk ykand computations have been performed for e 10ÿ3; 10ÿ2; 10ÿ1; 1; 101; 102. 

Q5. What is the criterion for the accuracy of the alternative ak?

If the accuracy criterion takes a non-negative value then all alternatives contained in A are ``correctly'' assigned for allk0 2 kÿ min k : ak2A fykg; k min k : ak2A fxkg :This criterion, however, takes into account the ``worst case'' only, i.e., the alternative for which the ELECTRE TRI model gives the most di erent assignment from the DM. 

Q6. What is the common procedure for comparing a to a category?

Pessimistic (or conjunctive) procedure: (a) compare a successively to bi, for i p; p ÿ 1; . . . ; 1, (b) bh being the ®rst pro®le such that aSbh, assign a to category Ch 1 a! 

Q7. What is the role of an interactive tool?

The role of an interactive tool is to help the DM to learn about his/her preferences and their possible representation in a speci®c aggregation model. 

Q8. What is the way to determine the weights of the assignment examples?

In order to determine a ``reasonable amount of information'' to infer the weights, the authors use the following experimental scheme: the optimization procedure is performed using di erent sets of assignment examples, whose size varies from 6 to 48 (10 sets for each size, see Section 5). 

Q9. What is the purpose of this experiment?

This experiment is a laboratory work, i.e., takes its material in a past real world case study to perform a posteriori computations in order to test the operational validity of the optimization model proposed in Section 4.