Nested probabilistic-numerical linguistic term sets in two-stage multi-attribute group decision making

Fuzzy linguistic approach is considered as an effective solution to accommodate uncertainties in qualitative decision making. In the face of increasingly complicated environment, we usually face the fact that multi-attribute group decision making contains nested information, and the whole process needs to be evaluated twice so that the experts can make full use of decision information to get more accurate result, and we call this kind of problem as two-stage multi-attribute group decision making (TSMAGDM). However, the existing linguistic approaches cannot represent such nested evaluation information to deal with the above situation. In this paper, a novel linguistic expression tool called nested probabilistic-numerical linguistic term set (NPNLTS) which considers both quantitative and qualitative information, is proposed to handle TSMAGDM. Based on which, some basic operational laws and aggregation operators are put forward. Then, an aggregation method and an extended TOPSIS method are developed respectively in TSMAGDM with NPNLTSs. Finally, an application case about strategy initiatives of HBIS GROUP on Supply-side Structural Reform is presented, and some analyses and comparisons are provided to validate the proposed methods.