Allowing agents to be imprecise: A proposal using multiple linguistic terms

Abstract

In this paper we propose a decision-making procedure where the agents judge the alternatives through linguistic terms such as 'very good', 'good', 'acceptable', etc. If the agents are not confident about their opinions, they can use a linguistic expression formed by several consecutive linguistic terms. To obtain a ranking on the set of alternatives, the method consists of three different stages. The first stage looks for the alternatives in which the overall opinion is closer to the ideal assessment. The overall opinion is developed by a distance-based process among the individual assessments. The next two stages form a tie-breaking process. Firstly by using a dispersion index based on the Gini coefficient, and secondly by taking into account the number of best-assessments. The main characteristics of the proposed decision-making procedure are analyzed.

Consensus-based clustering under hesitant qualitative assessments

“…Clearly, other metrics can be used, in particular the parameterized family introduced by Falcó et al [14]. The geodesic metric used in this paper, for simplicity reasons, is the degenerate case of the mentioned family, just when the parameters that penalize the imprecision are zero.…”

“…Then, the moderator may focus on these agents. Once a consensus threshold is reached, a group decision-making procedure can be carried out in order to rank the alternatives (within our framework those given by Falcó et al [13,14], for instance).…”

“…We now show some concepts and notation we need for introducing our proposal (for more details, see Falcó et al [14]). …”

“…In Falcó et al [13,14] the mentioned approach has been used for introducing and analyzing some voting systems where agents show their linguistic assessments over the alternatives under uncertainty.…”

“…For this reason, it is interesting to allow the agents to judge in a more imprecise way, giving them the option of assigning several linguistic terms 1 . Our approach concerning the imprecision is based on an adaptation of the absolute order of magnitude spaces introduced by Travé-Massuyès and Dague [31] and Travé-Massuyès and Piera [32]; more specifically in the extensions devised by Roselló et al [25,26,27] (see also Agell et al [1] and Falcó et al [13,14]). …”