The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry

With the Pandora's Box of the virtual reality (VR) being opened, it is undoubtedly a good choice for those companies that have no VR experience and want a share in the competitive marketplace to cooperate with a leading VR company. How to choose an appropriate leading company becomes a group decision-making (GDM) problem that we want to deal with. Whereas volatile decision-making environment conduces that the decision-making information of the aforementioned GDM problem cannot be expressed by traditional explicit values. Thus, we choose probabilistic uncertain linguistic term set (HILTS) which is one of the most emerging decision making tools and relatively manifests the unstable decision-making information as an instrument to address the GDM problem. Then this paper studies the consensus among the preference relations (PRs) and selects a suitable alternative for the aforementioned GDM problem. Firstly, we construct the probabilistic uncertain linguistic preference relation (PULPR) and the normalized PULPR. Secondly, the distance measure and similarity degree are defined to measure the consensus degree. Moreover, the two specific consensus processes are described separately. One is based on the distance measure between the individual PULPR and the group PULPR, the other is based on the similarity degree among the individual PULPR. Thirdly, by using the selection process in the light of the proposed possibility degree, two corresponding algorithms are proposed for solving the practical GDM problem. Finally, a practical case of choosing applicable VR company is used to demonstrate the efficiency of the two algorithms.