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The aim of multiple criteria decision aiding (MCDA) is to assist decision makers (DMs) to make rational decisions with respect to their preferences. In fact, the ranking approaches are the most used ones nowadays in the MCDA field because they are easy to understand by DMs and they are based on realistic assumptions. The hierarchical additive ratio assessment (ARAS-H) method is a ranking method. It represents an extension of the ARAS method in case of hierarchically structured criteria. However, most often, the DM is unable to provide precise performance values. Henceforth, in order to facilitate the task for him, he is asked to provide linguistic variables. Thus, the authors adopted the fuzzy logic. As a matter of fact, the fuzzy set theory takes into account the subjectivity of experts' ‘judgments.' In the light of the above, the fuzzy ARAS-H (F-ARAS-H) algorithm was developed as an extension of the ARAS-H method in a context of a fuzzy environment. To discuss the feasibility of the proposed algorithm, a case study on the selection of a green supplier was presented.

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In most of multicriteria aggregation methods, we need to elicit parameters that are generally determined directly by the decision-maker (DM). Direct assigning of parameters and criteria weights presents a crucial and difficult step in the decision-making process. However, this kind of information is too subjective and may affects the reliability of the results. To overcome this issue, we suggest a weighting method based on mathematical programming to incorporate the DM's preferences indirectly within the ARAS method.

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