Abstract
Recently, an extension of typical hesitant fuzzy element (HFE) called the ordered weighted hesitant fuzzy element (OWHFE) has been proposed to allow the membership of a given element is to be defined in terms of several possible values together with their importance weights. Moreover, the concept of probabilistic linguistic term sets (PLTSs) has been defined to extend hesitant fuzzy linguistic term sets (HFLTSs) by adding probabilities without loss of any original linguistic information. In fact, the concept of PLTS allows the membership of a given element is to be defined in terms of several possible linguistic values over an object together with the probabilistic information of the set of values. However, the PLTSs have some drawbacks in comparison to the newly defined concept OWHFEs, and such disadvantages of the PLTSs can be prevented by using the OWHFEs. This reveals the need of first defining the modified-PLTS (M-PLTS), and then transforming the M-PLTSs to the OWHFEs which will be the heart of this contribution. Finally, to demonstrate the advantage of the proposed methods, we implement again a number of practical problems that were previously associated with PLTSs.