A general class of simple majority decision rules based on linguistic opinions

In this paper we have introduced a class of decision rules related to simple majority, by considering individual intensities of preference. These intensities will be shown by means of linguistic labels. In order to compare the amount of opinion obtained by each alternative, we have considered the total ordered monoid generated by the sums of the original labels, according to an addition and an ordering. In this general framework different sets of linguistic labels can be employed and these sets can be represented by means of diverse mathematical objects. Moreover, on these mathematical representations of linguistic labels several orderings can be considered. Thus, flexibility is an important feature of this new class of group decision making procedures. Some examples of putting in practice the simple majority decision rules based on linguistic labels are provided, and the main properties of these voting systems are analyzed. It is worth emphasizing that these properties are satisfied for any total ordered monoid, regardless of the mathematical representation of linguistic labels or the ordering used to compare collective opinions.