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<p>The complex fuzzy set and (r, s, t)-Spherical fuzzy set serve as valuable extensions of various fuzzy structures, including fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, q-rung orthopair fuzzy sets, spherical fuzzy sets, and T-spherical fuzzy sets. In modelling some real-world problems, using complex values, which play a significant role in representing multidimensional data, is often more advantageous than using crisp values. In this study, set and arithmetic operations are redefined among two Crst-SFSs, and some properties regarding these operations are discussed. In addition, a Crst-SFN’s accuracy and score functions are redefined. Additionally, distance measure (DM)s using Hausdorff, Euclidean, and Hamming measures between two Crst-SFSs are put forward. Furthermore, a multi-criteria group decision-making (MCGDM) technique based on TOPSIS method using proposed score function and DMs is developed. A case study is presented to show how the suggested MCGDM approach can be used. Finally, a comparison is made among the current and novel methods.</p>

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Complex (r, s, t)-spherical fuzzy sets: a new approach to multi-criteria group decision-making based on the TOPSIS method

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Fatih Karamaz,
  • Faruk Karaaslan

摘要

The complex fuzzy set and (r, s, t)-Spherical fuzzy set serve as valuable extensions of various fuzzy structures, including fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, q-rung orthopair fuzzy sets, spherical fuzzy sets, and T-spherical fuzzy sets. In modelling some real-world problems, using complex values, which play a significant role in representing multidimensional data, is often more advantageous than using crisp values. In this study, set and arithmetic operations are redefined among two Crst-SFSs, and some properties regarding these operations are discussed. In addition, a Crst-SFN’s accuracy and score functions are redefined. Additionally, distance measure (DM)s using Hausdorff, Euclidean, and Hamming measures between two Crst-SFSs are put forward. Furthermore, a multi-criteria group decision-making (MCGDM) technique based on TOPSIS method using proposed score function and DMs is developed. A case study is presented to show how the suggested MCGDM approach can be used. Finally, a comparison is made among the current and novel methods.