A representative in group decision by means of the extended set of hesitant fuzzy linguistic term sets

Abstract

Hesitant fuzzy linguistic term sets were introduced to grasp the uncertainty existing in human reasoning when expressing preferences. In this paper, an extension of the set of hesitant fuzzy linguistic term sets is presented to capture differences between non-compatible preferences. In addition, an order relation and two closed operation over this set are also introduced to provide a lattice structure to the extended set of hesitant fuzzy linguistic term sets. Based on this lattice structure a distance between hesitant fuzzy linguistic descriptions is defined. This distance enables differences between decision makers to be quantified. Finally, a representative of a decision making group is presented as the centroid of the group based on the introduced distance.