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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2017019632
Forthcoming Article

Probability multi-valued linguistic neutrosophic sets for multi-criteria group decision-making

Nunu Wang
Central South University
Hongyu Zhang
Central South University


In view of diverse characteristics of decision makers (DMs) in multi-criteria group decision-making (MCGDM) problems, it is necessary to divide DMs into groups, so that DMs within the group are similar as far as possible and DMs between groups may have great difference. On this occasion, this paper introduces probability multi-valued linguistic neutrosophic sets (PMVLNSs) to depict group evaluation information that linguistic term sets (LTSs) allow DMs to evaluate more easily and accurately, and probability information can clearly reflect the opinion distribution of DMs within a group. This paper establishes a novel decision method with probability multi-valued linguistic neutrosophic numbers (PMVLNNs) to solve MCGDM problems in which the weight vectors of criteria and groups are completely unknown. First, the definition of PMVLNSs is characterized. Second, the comparison method, the projection measurement, and the aggregation operator of PMVLNNs are proposed. Furthermore, a novel extended TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method with PMVLNNs for MCGDM problems is developed. Finally, an illustrative example is conducted to demonstrate the application of the proposed method, and a comparison with several extant methods is also presented to verify its feasibility.