Soft ELECTRE TRI outranking method based on belief functions

Main decisions problems can be described into choice, ranking or sorting of a set of alternatives. The classical ELECTRE TRI (ET) method is a multicriteria-based outranking sorting method which allows to assign alternatives into a set of predetermined categories. ET method deals with situations where indifference is not transitive and solutions can sometimes appear uncomparable. ET suffers from two main drawbacks: 1) it requires an arbitrary choice of λ-cut step to perform the outranking of alternatives versus profiles of categories, and 2) an arbitrary choice of attitude for final assignment of alternatives into the categories. ET finally gives a final binary (hard) assignment of alternatives into categories. In this paper we develop a soft version of ET method based on belief functions which circumvents the aforementioned drawbacks of ET and allows to obtain both a soft (probabilistic) assignment of alternatives into categories and an indicator of the consistency of the soft solution. This Soft-ET approach is applied on a concrete example to show how it works and to compare it with the classical ET method.