RETRACTED: An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information

Abstract

In this paper, we develop an interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making (P-HFMAGDM) with incomplete weight information, in which the assessments provided by the decision makers for alternatives over attributes are expressed by probabilistic hesitant f uzzy elements (P-HFEs) and the weight information on attributes is partly known. Firstly, we propose the axiomatic definition of distance measures for P-HFEs, and then develop several kinds of distance measures for P-HFEs. Afterwards, we put forward the probabilistic hesitant fuzzy positive ideal solution and the probabilistic hesitant fuzzy negative ideal solution, respectively. By using the distance measures for P-HFEs, we define the closeness coefficients of alternatives, based on which we further establish a multi-objective optimization model to handle the P-HFMAGDM problems with incomplete weight information. Additionally, to facilitate the decision makers to provide new preference information or modify the previous preference information, an interactive approach is developed to deal with the P-HFMAGDM problems with incomplete weight information. Finally, a practical example involving the evaluation of the VR project declaration is provided to illustrate our approach.