Abstract
We investigate the multiple attribute group material selection problems in which the attribute values take the form of interval 2-tuple linguistic information. Firstly, some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop some interval 2-tuple linguistic aggregation operators called interval 2-tuple hybrid harmonic mean (ITHHM) operator, induced interval 2-tuple ordered weighted harmonic mean (I-ITOWHM) operator, and induced interval 2-tuple hybrid harmonic mean (I-ITHHM) operator and study some desirable properties of the I-ITOWHM operator. In particular, all these operators can be reduced to aggregate 2-tuple linguistic variables. Based on the I-ITHHM and the ITWHM (interval 2-tuple weighted harmonic mean) operators, an approach to multiple attribute group decision-making with interval 2-tuple linguistic information is proposed. Finally, a practical application to material selection problem is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Highlights
The 2-tuple linguistic representation model, characterized by a linguistic term and a numeric value, was developed by Herrera and Martınez [1] based on the concept of symbolic translation
Motivated by the idea of harmonic mean operators [30, 31], in this paper, we develop some interval 2-tuple linguistic harmonic mean operators, such as the interval 2-tuple hybrid harmonic mean (ITHHM) operator, the induced interval 2-tuple ordered weighted harmonic mean (I-ITOWHM) operator, and the induced interval 2-tuple hybrid harmonic mean (I-ITHHM) operator
Motivated by the formulas proposed by Xu [35, 36], the comparison of linguistic information represented by interval 2-tuples is implemented on the basis of the possibility degree of the interval 2-tuple linguistic variables
Summary
The 2-tuple linguistic representation model, characterized by a linguistic term and a numeric value, was developed by Herrera and Martınez [1] based on the concept of symbolic translation. Many researchers have investigated linguistic multiple attribute group decision-making (MAGDM) problems and proposed lots of methods to deal with linguistic evaluation information. These linguistic computational models can be mainly classified into three types [3, 4]: the method based on membership functions, the method based on linguistic symbols, and the method based on linguistic 2-tuples.
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