The prametric-based GDM selection procedure under linguistic assessments

The prametric-based procedure is a group decision making (GDM) selection process minimizing a consensus gap indicator, which is not a metric but a prametric. The prametric is an 'almost metric' which does not necessarily satisfy the triangle inequality but able to describe the consensus intransitivity in GDM. This paper considers the procedure under a linguistic situation, where the individuals preferences are provided as linguistic preference relations. The procedure contains two main stages. The first stage looks for the individual's ties-permitted ordinal rankings from the individual's opinions. In order to do this, we introduce an acceptable consistency criterion for linguistic preference relations and show some related properties. If the linguistic preference relation is acceptable, we then obtain the ties-permitted ordinal ranking directly. Otherwise, the ties-permitted ordinal ranking will be deduced by minimizing a consensus gap. The second stage looks for the final solution sets of alternatives by minimizing the gap between a potential solution and the rankings obtained in the first stage. Some illustrative examples are included.