A vertical ranking technique for linguistic hesitant fuzzy sets

By the help of the current contribution, we are interested to present a different technique compared to the exiting ones for ranking linguistic hesitant fuzzy sets (LHFSs). In the existing techniques that are referred hereafter to as the horizontal ranking procedures of LHFSs, we sum up all the multiplications of subscript of linguistic variable by the score value of the corresponding HFS. Meanwhile, through the vertical ranking technique of LHFSs, for a fixed subscript of linguistic variable, we compare firstly the corresponding HFSs using the existing raking methods to achieve the corresponding individual preference matrix. Then, all the individual preference matrices are multiplied by the subscript of that corresponding linguistic variable to get the aggregated and collective preference matrix. Eventually, the final ranking order of LHFSs is extracted by the use of collective majority decision rule. By the way, as will be shown later, all the horizontal ranking techniques suffer drawbacks to some extent, and this is the motivation for enriching the theory of ranking LHFSs by introducing the vertical ranking technique.