2-Tuple linguistic harmonic operators and their applications in group decision making

Harmonic mean is reciprocal of arithmetic mean of reciprocal, which is a conservative average to be used to provide for aggregation lying between max and min operators. In this paper, we develop some new linguistic aggregation operators such as 2-tuple linguistic harmonic (2TLH) operator, 2-tuple linguistic weighted harmonic (2TLWH) operator, 2-tuple linguistic ordered weighted harmonic (2TLOWH) operator, and 2-tuple linguistic hybrid harmonic (2TLHH) operator, which can be utilized to aggregate preference information taking the form of linguistic variables, and then study some desirable properties of the operators. Based on the 2TLWH and 2TLHH operators, we present an approach to multiple attribute decision making with 2-tuple linguistic information. Finally, illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness by comparing with the existing approaches.