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Similarity Measures for Fractional Orthotriple Fuzzy Sets Using Cosine and Cotangent Functions and Their Application in Accident Emergency Response

Author

Listed:
  • Muhammad Naeem

    (Deanship of Combined First Year Umm Al-Qura University Makkah, Mecca, P.O. Box 715, Saudi Arabia)

  • Muhammad Qiyas

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan)

  • Mohammed M. Al-Shomrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 802000, Jeddah 21589, Saudi Arabia)

  • Saleem Abdullah

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan)

Abstract

The fractional orthotriple fuzzy set (FOFS) is more generalized than the spherical fuzzy set (SFS) and picture fuzzy set (PFS) to cope with awkward and complex information in fuzzy set (FS) theory. The FOFS is a more powerful technique with respect to the existing drawbacks because of its conditions, i.e., the sum of the f powers of positive, neutral, and negative grades is bounded to [ 0 , 1 ] . With the advantages of the FOFS, in this paper, we study the basic definitions and some existing similarity measures (SMs) of intuitionistic fuzzy sets (IFSs), PFSs, Pythagorean fuzzy sets (PyFSs) and SFSs. The existing approaches have certain limitations and cannot be applied to problems that are in the form of FOFSs. The goal of this paper is to propose the idea of some new SMs including cosine SMs for FOFSs, SMs for FOFSs based on the cosine function, and SMs for FOFSs based on the cotangent function. Further, some weighted SMs (WSMs) are also proposed for which the weight of the attributes is considered. Then, we apply these SMs and WSMs to the pattern recognition problem. Finally, the comparative study of the new SMs for FOFSs is established with existing SMs, and also, some advantages of the proposed work are discussed.

Suggested Citation

  • Muhammad Naeem & Muhammad Qiyas & Mohammed M. Al-Shomrani & Saleem Abdullah, 2020. "Similarity Measures for Fractional Orthotriple Fuzzy Sets Using Cosine and Cotangent Functions and Their Application in Accident Emergency Response," Mathematics, MDPI, vol. 8(10), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1653-:d:419026
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    References listed on IDEAS

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    1. Guiwu Wei, 2018. "Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making," International Journal of Decision Support System Technology (IJDSST), IGI Global, vol. 10(2), pages 40-64, April.
    2. Shouzhen Zeng & Harish Garg & Muhammad Munir & Tahir Mahmood & Azmat Hussain, 2019. "A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells," Energies, MDPI, vol. 12(23), pages 1-26, November.
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