Using consensus and distances between generalized multi-attribute linguistic assessments for group decision-making

Consensus-based clustering under hesitant qualitative assessments

“…l 5 very bad bad acceptable good very good Taking into account the approach introduced in Roselló et al [27], the set of all the linguistic expressions can be represented by a graph G L . In the graph, the lowest layer represents the linguistic terms l h ∈ L ⊂ L, the second layer represents the linguistic expressions created by two consecutive linguistic terms [l h , l h+1 ], the third layer represents the linguistic expressions generated by three consecutive linguistic terms [l h , l h+2 ], and so on up to last layer where we represent the linguistic expression [l 1 , l g ].…”

“…When an agent is confident about his opinion on an alternative, he can assign a linguistic term l h ∈ L to this alternative. However, if he is unconfident about his opinion, he might use a linguistic expression [l h , l k ] ∈ L, with h < k. For more details, see Roselló et al [25,26,27].…”

“…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]). …”

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

“…Our proposal concerning the imprecision is based on an adaptation of the absolute order of magnitude spaces introduced in Travé-Massuyès and Dague [29], and Travé-Massuyès and Piera [30]; more specifically in the extensions devised by Roselló et al [24,25,26].…”

“…Adopting the treatment introduced in Roselló et al [26], the set of all the linguistic expressions can be represented by a graph G L . In the graph, the lowest layer represents the linguistic terms l h ∈ L ⊂ L, the second layer represents the linguistic expressions created by two consecutive linguistic terms [l h , l h+1 ], the third layer represents the linguistic expressions created by three consecutive linguistic terms [l h , l h+2 ], and so on up to last layer where we represent the linguistic expression [l 1 , l g ].…”