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TOPSIS Method Based on Correlation Coefficient and Entropy Measure for Linguistic Pythagorean Fuzzy Sets and Its Application to Multiple Attribute Decision Making

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  • Mingwei Lin
  • Chao Huang
  • Zeshui Xu

Abstract

The linguistic Pythagorean fuzzy set (LPFS) is an important implement for modeling the uncertain and imprecise information. In this paper, a novel TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method is proposed for LPFSs based on correlation coefficient and entropy measure. To this end, the correlation coefficient is proposed for the relationship measurement between LPFSs. Afterwards, two entropy measures are developed to calculate the attribute weight information. Then, a novel linguistic Pythagorean fuzzy TOPSIS (LPF-TOPSIS) method is proposed to solve multiple attribute decision-making problems. Finally, the LPF-TOPSIS method is applied to handle a case concerning the selection of firewall productions, and then, a case concerning the security evaluation of computer systems is given to conduct the comparative analysis between the proposed LPF-TOPSIS method and previous decision-making methods for validating the superiority of the proposed LPF-TOPSIS method.

Suggested Citation

  • Mingwei Lin & Chao Huang & Zeshui Xu, 2019. "TOPSIS Method Based on Correlation Coefficient and Entropy Measure for Linguistic Pythagorean Fuzzy Sets and Its Application to Multiple Attribute Decision Making," Complexity, Hindawi, vol. 2019, pages 1-16, October.
    • Handle: RePEc:hin:complx:6967390
    DOI: 10.1155/2019/6967390
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    References listed on IDEAS

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    1. Mingwei Lin & Jiuhan Wei & Zeshui Xu & Riqing Chen, 2018. "Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators," Complexity, Hindawi, vol. 2018, pages 1-24, November.
    2. Harish Garg, 2018. "Analysis of an industrial system under uncertain environment by using different types of fuzzy numbers," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(2), pages 525-538, April.
    3. Mingwei Lin & Zeshui Xu & Yuling Zhai & Zhiqiang Yao, 2018. "Multi-attribute group decision-making under probabilistic uncertain linguistic environment," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(2), pages 157-170, February.
    4. Huimin Zhang, 2014. "Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, April.
    5. Chao Zhang & Deyu Li & Yimin Mu & Dong Song, 2018. "A Pythagorean Fuzzy Multigranulation Probabilistic Model for Mine Ventilator Fault Diagnosis," Complexity, Hindawi, vol. 2018, pages 1-19, October.
    6. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
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