Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design
<inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>spherical fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF) sets are a significant advancement in fuzzy set (...
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2024-01-01
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| Online Access: | https://ieeexplore.ieee.org/document/10509687/ |
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| author | Lin Kang Salma Khan Muhammad Rahim Kamal Shah Thabet Abdeljawad |
| author_facet | Lin Kang Salma Khan Muhammad Rahim Kamal Shah Thabet Abdeljawad |
| author_sort | Lin Kang |
| collection | DOAJ |
| description | <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>spherical fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF) sets are a significant advancement in fuzzy set (FS) theory, providing an effective way to describe hesitation inside a set. This development goes beyond membership degrees (MDs) by incorporating three parameters (p, q and r) that shape and define the spread of FS. The presence of these parameters makes <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF sets ideal for dealing with complicated decision-making (DM) scenarios in a wide range of applications. In this paper, we proposed a new reliable method for smart DM in logo design projects that uses <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF Einstein aggregation operators (AOs). First, we present the <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF Einstein operators, which are accomplished of capturing the relationship and interrelationship of numerous criteria while making decisions on logo design, including originality, relevance, beauty, and usability. Next, we use the proposed framework, a multi-criteria decision analysis tool, to rank the choices. We demonstrate the practical application and efficiency of our method in a scenario in which a team of three designers is entrusted with developing five different logo styles for diverse enterprises. Moreover, we compare proposed procedure with some existing methods, demonstrating its advantages in terms of precision and reliability. |
| format | Article |
| id | doaj-art-05ed6f69bcaf4d50817430a878cf6d85 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-05ed6f69bcaf4d50817430a878cf6d852025-02-12T00:01:06ZengIEEEIEEE Access2169-35362024-01-0112683936840910.1109/ACCESS.2024.339469410509687Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo DesignLin Kang0Salma Khan1https://orcid.org/0000-0003-1840-2764Muhammad Rahim2https://orcid.org/0000-0003-0064-0414Kamal Shah3Thabet Abdeljawad4https://orcid.org/0000-0002-8889-3768Jiangsu Normal University Kewen College, Xuzhou, ChinaDepartment of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia<inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>spherical fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF) sets are a significant advancement in fuzzy set (FS) theory, providing an effective way to describe hesitation inside a set. This development goes beyond membership degrees (MDs) by incorporating three parameters (p, q and r) that shape and define the spread of FS. The presence of these parameters makes <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF sets ideal for dealing with complicated decision-making (DM) scenarios in a wide range of applications. In this paper, we proposed a new reliable method for smart DM in logo design projects that uses <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF Einstein aggregation operators (AOs). First, we present the <inline-formula> <tex-math notation="LaTeX">$p,q,r-$ </tex-math></inline-formula>SF Einstein operators, which are accomplished of capturing the relationship and interrelationship of numerous criteria while making decisions on logo design, including originality, relevance, beauty, and usability. Next, we use the proposed framework, a multi-criteria decision analysis tool, to rank the choices. We demonstrate the practical application and efficiency of our method in a scenario in which a team of three designers is entrusted with developing five different logo styles for diverse enterprises. Moreover, we compare proposed procedure with some existing methods, demonstrating its advantages in terms of precision and reliability.https://ieeexplore.ieee.org/document/10509687/p, q, r–spherical fuzzy setEinstein operationsaggregation operatorsdecision-makingoptimization |
| spellingShingle | Lin Kang Salma Khan Muhammad Rahim Kamal Shah Thabet Abdeljawad Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design IEEE Access p, q, r–spherical fuzzy set Einstein operations aggregation operators decision-making optimization |
| title | Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design |
| title_full | Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design |
| title_fullStr | Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design |
| title_full_unstemmed | Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design |
| title_short | Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design |
| title_sort | development italic p italic italic q italic italic r italic x2013 spherical fuzzy einstein aggregation operators application in decision making in logo design |
| topic | p, q, r–spherical fuzzy set Einstein operations aggregation operators decision-making optimization |
| url | https://ieeexplore.ieee.org/document/10509687/ |
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