Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making
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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/538261 |
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| author | Liyuan Zhang Xuanhua Xu Li Tao |
| author_facet | Liyuan Zhang Xuanhua Xu Li Tao |
| author_sort | Liyuan Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e5f02e0936874ea584fae7563455a0a3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e5f02e0936874ea584fae7563455a0a32025-02-03T05:49:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/538261538261Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-MakingLiyuan Zhang0Xuanhua Xu1Li Tao2School of Business, Central South University, Changsha, Hunan 410083, ChinaSchool of Business, Central South University, Changsha, Hunan 410083, ChinaSchool of Science, Shandong University of Technology, Zibo, Shandong 255049, ChinaWe 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.http://dx.doi.org/10.1155/2013/538261 |
| spellingShingle | Liyuan Zhang Xuanhua Xu Li Tao Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making Journal of Applied Mathematics |
| title | Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making |
| title_full | Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making |
| title_fullStr | Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making |
| title_full_unstemmed | Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making |
| title_short | Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making |
| title_sort | some similarity measures for triangular fuzzy number and their applications in multiple criteria group decision making |
| url | http://dx.doi.org/10.1155/2013/538261 |
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