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Dual hesitant fuzzy set (DHFS), which permits the possible membership degrees and non-membership degrees of an element having sets of values in [0,1], is considered as a powerful tool to express uncertain information in the process of multiple attribute group decision making (MAGDM). In this paper, we study the MAGDM problems in which the attribute values take the form of dual hesitant fuzzy elements and the weights of attributes and decision makers take the form of real numbers. Firstly, the normalized Hamming distance of the dual hesitant fuzzy elements is defined. Then, a new method for dealing MAGDM problems under dual hesitant fuzzy environment is proposed on the basis of grey relational analysis (GRA) theory. For the incompletely known and completely unknown information of attribute weight, some optimization models are established to determine the weights of attributes. Finally, a numerical example of investment alternative selection is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

We investigate the multi-attribute group decision making (MAGDM) problems in which the attribute values provided by the decision makers take the form of intuitionistic trapezoid fuzzy linguistic (ITrFL) information considering the uncertainty and inaccuracy of input arguments. Some new power aggregation operators called intuitionistic trapezoid fuzzy linguistic power average (ITrFLPA) operator, intuitionistic trapezoid fuzzy linguistic power weighted average (ITrFLPWA) operator, intuitionistic trapezoid fuzzy linguistic power ordered weighted average (ITrFLPOWA) operator, intuitionistic trapezoid fuzzy linguistic power hybrid weighted average (ITrFLPHWA) operator, intuitionistic trapezoid fuzzy linguistic power geometric (ITrFLPG) operator, intuitionistic trapezoid fuzzy linguistic power weighted geometric (ITrFLPWG) operator, intuitionistic trapezoid fuzzy linguistic power ordered weighted geometric (ITrFLPOWG) operator and intuitionistic trapezoid fuzzy linguistic power hybrid weighted geometric (ITrFLPHWG) operator are proposed. Then, we study some desirable properties of the proposed operators, such as idempotency, commutativity and boundedness. In addition, two novel approaches based on the proposed operators are developed to solve MAGDM problems with intuitionistic trapezoid fuzzy linguistic information. Finally, a numerical example is provided to verify the feasibility of the proposed approaches. [ABSTRACT FROM AUTHOR]