Social Choice Voting with Linguistic Preferences and Difference in Support

A new aggregation rule in social choice voting with linguistic intensities of preferences between pairs of alternatives is introduced. This new aggregation rule leads to the definition of linguistic majorities with difference in support under which an alternative defeats another if the first one reaches a concrete collective preference support fixed before the election process. This new rule extends existing rules from the context of crisp and reciprocal [0,1]-valued preferences to the framework of linguistic preferences. Both possible representation formats of linguistic information are addressed: fuzzy sets and 2-tuples. The linguistic majorities constitute a class of majority rules because they generalize all the possible majority rules by adjusting the required threshold of support.