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By combining picture fuzzy set and 2-tuple linguistic representation model, Wei et al. (Soft Comput 22(3):989–1002, 2018) proposed the concept of picture 2-tuple linguistic set and presented some operational laws of picture 2-tuple linguistic numbers (P2TLNs). On the basis of operational laws of P2TLNs, some picture 2-tuple linguistic aggregation operators have been further developed. However, some operational laws and results derived by aggregation operators proposed by Wei et al. (Soft Comput 22(3):989–1002, 2018) are conflict with definition of picture 2-tuple linguistic number (P2TLN). In this short note, we propose some novel operational laws of P2TLNs and develop one adjusted picture 2-tuple linguistic aggregation operator, i.e., the adjusted picture 2-tuple linguistic weighted averaging operator. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute group decision making (MAGDM) problems in which the assessment values of attributes take the form of interval-valued hesitant uncertain linguistic elements, a novel MAGDM method is proposed in this paper. Firstly, the concept, operational laws and score function of interval-valued hesitant uncertain linguistic elements (IVHULEs) are introduced. Then, based on the operational laws of IVHULEs, some generalized aggregation operators are proposed for aggregating the interval-valued hesitant uncertain linguistic information, including the generalized interval-valued hesitant uncertain linguistic weighted aggregation operators, the generalized interval-valued hesitant uncertain linguistic ordered weighted aggregation operators and the generalized interval-valued hesitant uncertain linguistic hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed. Based on the proposed operators, an approach to multiple attribute group decision making with unknown weight information is developed under interval-valued hesitant uncertain linguistic environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In the multi-attribute decision-making (MADM) problems, decision makers refer to the extreme attribute values in general when evaluating the alternatives. However, in the real world, the ideal solution may lie in somewhere between the extreme values. The recently proposed reference ideal method (RIM) is able to solve the problem rightly. This study aims at developing a novel MADM framework combining best–worst method (BWM), maximizing deviation method (MDM), and RIM under Z-number environment. In this framework, Z-number is used to depict the inherent uncertainty and reliability of information in the decision makers' judgments. And BWM and MDM are combined to determine the comprehensive attribute weights, in which BWM is utilized to obtain the subjective weights, while MDM is utilized to obtain the objective weights. In addition, Z-RIM is proposed by extending the traditional RIM under Z-number environment, which is employed for ranking the alternatives. An illustrative example of cloud service selection problem is implemented to illustrate the proposed framework. By comparison analysis, we demonstrate that Z-RIM can not only avoid rank reversal problem, but also generate reasonable results during the MADM processes. [ABSTRACT FROM AUTHOR]