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Mathematical Problems in Engineering
Volume 2013, Article ID 597671, 11 pages
Research Article

A Multiple Attribute Decision Making Method Based on Uncertain Linguistic Heronian Mean

1College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2School of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243002, China
3Logistics School, Linyi University, Linyi 276000, China

Received 2 August 2013; Accepted 24 August 2013

Academic Editor: Wei-Chiang Hong

Copyright © 2013 Xiaodi Liu 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.


The Heronian mean is a useful aggregation operator which can capture the interrelationship of the input arguments. In this paper, we develop some Heronian means based on uncertain linguistic variables, such as the generalized uncertain linguistic Heronian mean (GULHM) and uncertain linguistic geometric Heronian mean (ULGHM), and some of their desirable properties are also investigated. Considering the different importance of the input arguments, we define the generalized uncertain linguistic weighted Heronian mean (GULWHM) and uncertain linguistic weighted geometric Heronian mean (ULWGHM). Then, a method of multiple attribute decision making under uncertain linguistic environment is presented based on the GULWHM or the ULWGHM. In the end, an example is given to demonstrate the effectiveness and feasibility of the proposed method.