Consensus-based robust decision making methods under a novel study of probabilistic uncertain linguistic information and their application in Forex investment.

The probabilistic uncertain linguistic terms set (PULTS) is an effective tool to depict uncertain linguistic opinions of individuals or groups in the procedure of decision making. Motivated by the power of PULTS and the linguistic scale function, this study aims to propose robust techniques to solve multi-attribute group decision making problems with uncertain linguistic evaluations. To enrich calculation and enhance the flexibility of PULTS, we first generalize the aggregation formula to fuse opinions of decision makers represented as PULTSs and secondly derive adjusting rule of probability to adjust the probability distribution of two or more than two probabilistic uncertain elements (PULEs) into the same probability distribution. Novel operations of PULTSs are designed based on the adjusting rule of probability distribution and linguistic scale function for the semantics of linguistic terms. Many related properties of these operations are also discussed. New score function and deviation degree of PULEs are also developed to compare PULEs. Two aggregation operators i.e., probabilistic uncertain linguistic averaging (PULWA) operator and probabilistic uncertain linguistic geometric (PULWG) operator are also redefined in terms of novel operations. In addition, a series of distance measure is defined to overcome the shortcomings of existing ones. After defining a correlation measure, the probabilistic uncertain linguistic (PUL)-consensus reaching method (in which two specific consensus approaches are described separately) is put forward to refine the consensus level of a group. To suit the needs of different semantics, two robust decision making methods named as consensus-based PUL-gained and lost dominance score method and consensus-based PUL-aggregation method are proposed. Finally, a case study concerning the selection of the best commodity for investment in Forex is conducted to illustrate the practicality of the proposed methods. Lastly, a detailed comparative analysis is done with the existing technique to highlight the improvements and advantages of proposed work. [ABSTRACT FROM AUTHOR]