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Two linguistic-based voting systems have been introduced in recent years, namely: Majority Judgement (Balinski and Laraki in http://ceco.polytechnique.fr/ jugement-majoritaire.html, 2007a) and Range Voting (Smith in http://www.math. temple.edu/~wds/homepage/rangevote.pdf, 2000). The keys for them are aggregation procedures based on the median and the arithmetic mean of the grades assessed to the alternatives, respectively. In this paper a comprehensive framework based on centered OWA operators (Yager in Soft Comput 11:631-639, 2007a) and the 2-tuple model (Herrera and Martínez in IEEE Trans Fuzzy Syst 8: [746][747][748][749][750][751][752] 2000) is provided to enclose such distinct approaches. In addition, we show how to avoid some drawbacks of Majority Judgement and Range Voting by means of the use of suitable aggregation functions.

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