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Journal of Applied Mathematics
Volume 2013, Article ID 538261, 7 pages
Research Article

Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making

1School of Business, Central South University, Changsha, Hunan 410083, China
2School of Business, Shandong University of Technology, Zibo, Shandong 255049, China
3School of Science, Shandong University of Technology, Zibo, Shandong 255049, China

Received 19 September 2012; Accepted 11 March 2013

Academic Editor: Saeid Abbasbandy

Copyright © 2013 Liyuan Zhang 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 propose some similarity measures between two triangular fuzzy numbers (TFNs) based on the vector similarity measures in vector space, which can be used to aggregate the decision information with TFNs. A methodology for multiple criteria group decision-making (MCGDM) problems with triangular fuzzy information is proposed; the criteria values take the form of linguistic values, which can be converts to TFNs. According to the weighted similarity measures between each alternative and ideal alternative, it is easy to rank alternatives and select the most desirable alternative. Finally, we apply the proposed methods to an illustrative example of MCGDM; the numerical results show that our method is effective and practical. For comparison, we also apply our similarity measures method to solve the fuzzy decision-making problem in Wei (2011); our method has simpler computation and gets the same results more rapidly than the FLOWHM method.