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TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Author

Listed:
  • Zeeshan Ali

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Tahir Mahmood

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Miin-Shen Yang

    (Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan)

Abstract

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1739-:d:425979
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    References listed on IDEAS

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    1. 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.
    2. Miin-Shen Yang & Zahid Hussain & Mehboob Ali, 2020. "Belief and Plausibility Measures on Intuitionistic Fuzzy Sets with Construction of Belief-Plausibility TOPSIS," Complexity, Hindawi, vol. 2020, pages 1-12, August.
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    4. 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.
    5. Lvqing Bi & Zhiqiang Zeng & Bo Hu & Songsong Dai, 2019. "Two Classes of Entropy Measures for Complex Fuzzy Sets," Mathematics, MDPI, vol. 7(1), pages 1-10, January.
    6. Qianli Zhou & Hongming Mo & Yong Deng, 2020. "A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
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    Cited by:

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    2. Maria Akram & Kifayat Ullah & Goran Ćirović & Dragan Pamucar, 2023. "Algorithm for Energy Resource Selection Using Priority Degree-Based Aggregation Operators with Generalized Orthopair Fuzzy Information and Aczel–Alsina Aggregation Operators," Energies, MDPI, vol. 16(6), pages 1-22, March.
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    6. Mujab Waqar & Kifayat Ullah & Dragan Pamucar & Goran Jovanov & Ðordje Vranješ, 2022. "An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators," Energies, MDPI, vol. 15(11), pages 1-23, May.

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