Choice functions and mechanisms for linguistic preference relations

The problem of finding a solution set of alternatives when a linguistic preference relation represents a collective preference is analyzed following two research lines, choice functions and mechanisms. Four classical choice sets of alternatives for a linguistic preference relation are presented and some relations between them are pointed out. The concept of linguistic choice function as a tool to derive linguistic choice sets of alternatives is introduced and some particular linguistic choice functions are presented together with a study of their rationality properties. On the other hand, two types of linguistic choice mechanisms to derive solution sets of alternatives from linguistic choice functions are introduced: simple and composite ones. The concept of linguistic covering relation is introduced with a view to allow us the design of consistent linguistic choice mechanisms which may achieve more precise and coherent solution sets of alternatives.