Integrating second-order effects in ELECTRE methods with an interval-based approach

Abstract

Evolving from earlier versions, the ELECTRE methods achieved their most popular model with the fuzzy outranking relation of ELECTRE III. In more recent papers, the effects of reinforced preference, interacting criteria, and the relative strength of the discordance coalition have enhanced the original ELECTRE III. However, these enhancements were proposed separately. This paper has the merit of combining ELECTRE III with its enhancements in a comprehensive model. Although the extended model is more sophisticated and complex, its application may be necessary to accurately reflect the decision maker’s preferences when at least two of the three modifications to the original ELECTRE III cannot be neglected. Since the comprehensive model is more complex than the original one and may contain numerous parameters that are unfamiliar to decision-makers, its construction may be a challenging cognitive task for them. To alleviate this task and handle imperfect knowledge about model parameters and criteria performance levels, this paper proposes an interval-based approach. Thus, as a result of this paper, the pair Decision Maker–Decision Analyst can opt for one of two models: i) the extended ELECTRE III, where parameters and criteria are real numbers; or ii) the interval-based generalization of ELECTRE III, where parameters and criteria can be interval numbers. Both models combine the effects of reinforced preference, interacting criteria, and the relative strength of the discordance coalition. The interval model is more complex but the direct elicitation of its parameters is easier. The outranking relations provided by both approaches are useful for selection and ranking purposes, as well as multiple criteria ordinal classification. The ordinal classification methods based on these relations fulfill the consistency properties required by the ELECTRE TRI family. The new proposal is illustrated by two examples: the first is a simple ordinal classification problem with real numbers; the second example, with the use of interval numbers, comes from a real-world decision problem, revisiting a case study regarding the assessment of the performance of countries from the Organization for Economic Co-operation and Development (OECD).