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Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making

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  • Miin-Shen Yang
  • Zahid Hussain

Abstract

The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In the present paper, we have used both probabilistic and nonprobabilistic types to calculate fuzzy entropy of PFSs. Firstly, a probabilistic-type entropy measure for PFSs is proposed and then axiomatic definitions and properties are established. Secondly, we utilize a nonprobabilistic-type with distances to construct new entropy measures for PFSs. Then a min–max operation to calculate entropy measures for PFSs is suggested. Some examples are also used to demonstrate suitability and reliability of the proposed methods, especially for choosing the best one/ones in structured linguistic variables. Furthermore, a new method based on the chosen entropies is presented for Pythagorean fuzzy multicriterion decision making to compute criteria weights with ranking of alternatives. A comparison analysis with the most recent and relevant Pythagorean fuzzy entropy is conducted to reveal the advantages of our developed methods. Finally, this method is applied for ranking China-Pakistan Economic Corridor (CPEC) projects. These examples with applications demonstrate practical effectiveness of the proposed entropy measures.

Suggested Citation

  • Miin-Shen Yang & Zahid Hussain, 2018. "Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making," Complexity, Hindawi, vol. 2018, pages 1-14, November.
    • Handle: RePEc:hin:complx:2832839
    DOI: 10.1155/2018/2832839
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    References listed on IDEAS

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    1. Lifei Zhang & Fanyong Meng, 2018. "An Approach to Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on the Generalized Shapley-Choquet Integral," Complexity, Hindawi, vol. 2018, pages 1-19, June.
    2. Runtong Zhang & Jun Wang & Xiaomin Zhu & Meimei Xia & Ming Yu, 2017. "Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making," Complexity, Hindawi, vol. 2017, pages 1-16, August.
    3. Peide Liu & Peng Wang, 2017. "Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 817-850, May.
    4. Luis Pérez-Domínguez & Luis Alberto Rodríguez-Picón & Alejandro Alvarado-Iniesta & David Luviano Cruz & Zeshui Xu, 2018. "MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making," Complexity, Hindawi, vol. 2018, pages 1-10, April.
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    Cited by:

    1. Zeeshan Ali & Tahir Mahmood & Miin-Shen Yang, 2020. "TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    2. Shio Gai Quek & Ganeshsree Selvachandran & Florentin Smarandache & J. Vimala & Son Hoang Le & Quang-Thinh Bui & Vassilis C. Gerogiannis, 2020. "Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    3. 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.
    4. Hari Darshan Arora & Anjali Naithani, 2022. "Logarithmic similarity measures on Pythagorean fuzzy sets in admission process," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 5-24.

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