An extension of the Electre I method for group decision-making under a fuzzy environment

TLDR: This study proposes an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs, and shows that contrary to the TOPSIS rankings, the electre approach reveals more useful information including the incomparability among the actions.

Abstract: Many real-world decisionproblems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers(DMs)where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis(MCDA)is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit,rational and efficient. One family of MCDA models uses what is known as "outranking relations" to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study,we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1)we address the gap in the Electre literature for problems involving conflicting systems of criteria,uncertainty and imprecise information;(2)we extend the Electre I method to take into account the uncertain,imprecise and linguistic assessments; (3)we define out ranking relations by pairwise comparisons and use decision graphs to determine which action is preferable,incomparable or indifferent in the fuzzy environment; (4)we show that contrary to the TOPSIS rankings,the Electre approach reveals more useful information including the incomparability among the actions;and (5)we provide a numerical example to elucidate the details of the proposed method.