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

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  • Liyuan Zhang
  • Xuanhua Xu
  • Li Tao

Abstract

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.

Suggested Citation

  • Liyuan Zhang & Xuanhua Xu & Li Tao, 2013. "Some Similarity Measures for Triangular Fuzzy Number and Their Applications in Multiple Criteria Group Decision-Making," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, March.
    • Handle: RePEc:hin:jnljam:538261
    DOI: 10.1155/2013/538261
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    Cited by:

    1. Chiuhsiang Joe Lin & Tariku Tamiru Belis & Tsai Chi Kuo, 2019. "Ergonomics-Based Factors or Criteria for the Evaluation of Sustainable Product Manufacturing," Sustainability, MDPI, vol. 11(18), pages 1-20, September.
    2. Dongxiao Niu & Hao Zhen & Min Yu & Keke Wang & Lijie Sun & Xiaomin Xu, 2020. "Prioritization of Renewable Energy Alternatives for China by Using a Hybrid FMCDM Methodology with Uncertain Information," Sustainability, MDPI, vol. 12(11), pages 1-26, June.
    3. Chiuhsiang Joe Lin & Tariku Tamiru Belis & Dino Caesaron & Bernard C. Jiang & Tsai Chi Kuo, 2020. "Development of Sustainability Indicators for Employee-Activity Based Production Process Using Fuzzy Delphi Method," Sustainability, MDPI, vol. 12(16), pages 1-31, August.
    4. Hari Darshan Arora & Anjali Naithani, 2023. "Some distance measures for triangular fuzzy numbers under technique for order of preference by similarity to ideal solution environment," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 701-719, June.
    5. M. Hajibabaei & J. Behnamian, 2023. "Fuzzy cleaner production in assembly flexible job-shop scheduling with machine breakdown and batch transportation: Lagrangian relaxation," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-26, July.

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