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As an extension of the classic fuzzy sets, Gündoğdu and Kahraman (J. Intell. Fuzzy Syst. 36:337–352, 2019) introduced the concepts of spherical fuzzy sets (SFSs). The SFSs are a direct extension of picture fuzzy sets where the sum of squares of membership, non-membership, and neutral degrees must not exceed 1. As an example, the membership degree of 0.7, neutral degree of 0.5, and non-membership degree of 0.5, cannot be presented as a picture fuzzy set as \(0.7 + 0.5 + 0.5 \ge 1\) . But this event can be presented as a spherical fuzzy set as \(\left( {0.7} \right)^{2} + \left( {0.5} \right)^{2} + \left( {0.5} \right)^{2} = 0.99 \le 1\) . In fact, spherical fuzzy sets contain most of the advantages of other extensions of the classical fuzzy sets (Gündoğdu and Kahraman in Eng. Appl. Artif. Intell. 85:307–323, 2019).

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Spherical Fuzzy Sets

  • 章节

  • 发表日期：

    2026年

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  • Ali Mahmoodirad,
  • Harish Garg,
  • Sadegh Niroomand

摘要

As an extension of the classic fuzzy sets, Gündoğdu and Kahraman (J. Intell. Fuzzy Syst. 36:337–352, 2019) introduced the concepts of spherical fuzzy sets (SFSs). The SFSs are a direct extension of picture fuzzy sets where the sum of squares of membership, non-membership, and neutral degrees must not exceed 1. As an example, the membership degree of 0.7, neutral degree of 0.5, and non-membership degree of 0.5, cannot be presented as a picture fuzzy set as \(0.7 + 0.5 + 0.5 \ge 1\) . But this event can be presented as a spherical fuzzy set as \(\left( {0.7} \right)^{2} + \left( {0.5} \right)^{2} + \left( {0.5} \right)^{2} = 0.99 \le 1\) . In fact, spherical fuzzy sets contain most of the advantages of other extensions of the classical fuzzy sets (Gündoğdu and Kahraman in Eng. Appl. Artif. Intell. 85:307–323, 2019).