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Advances in Materials Science and Engineering
Volume 2016, Article ID 7034938, 13 pages
Research Article

Some Interval 2-Tuple Linguistic Harmonic Mean Operators and Their Application in Material Selection

1School of Management, Shanghai University, Shanghai 200444, China
2School of Economics and Management, Tongji University, Shanghai 200092, China

Received 13 April 2016; Accepted 30 June 2016

Academic Editor: Charles C. Sorrell

Copyright © 2016 Meng-Meng Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.