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

Muhammad Naeem, Muhammad Qiyas, Mohammed M. Al-Shomrani and Saleem Abdullah
Additional contact information
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

Mathematics, 2020, vol. 8, issue 10, 1-19

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.

Keywords: fractional orthotriple fuzzy sets; fractional orthotriple fuzzy cosine similarity measure; fractional orthotriple fuzzy cotangent similarity measure; decision making (DM) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/10/1653/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/10/1653/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:10:p:1653-:d:419026

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().