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The aim of this paper is to analyze under which conditions Absolute Order-of-Magnitude and Relative Order-of-Magnitude models may be concordant and to determine the constraints which guarantee concordance. A graphical interpretation of the constraints is provided, bridging the absolute qualitative labels of two quantities into their corresponding relative relation(s), and conversely. The relative order of magnitude relations are then characterized in the absolute order-of-magnitude world.

Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.