Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets
Similarity and distance measures play important roles in fuzzy environments, helping to quantify the degree of similarity or concepts that may not have clear limits. They are used in various fields, including fuzzy logic, fuzzy clustering, and fuzzy decision-making. The cubic Fermatean fuzzy set (CF...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-07-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682300340X |
| _version_ | 1797803978920034304 |
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| author | Muhammad Rahim Harish Garg Fazli Amin Luis Perez-Dominguez Ahmed Alkhayyat |
| author_facet | Muhammad Rahim Harish Garg Fazli Amin Luis Perez-Dominguez Ahmed Alkhayyat |
| author_sort | Muhammad Rahim |
| collection | DOAJ |
| description | Similarity and distance measures play important roles in fuzzy environments, helping to quantify the degree of similarity or concepts that may not have clear limits. They are used in various fields, including fuzzy logic, fuzzy clustering, and fuzzy decision-making. The cubic Fermatean fuzzy set (CFFS), which is a type of fuzzy set (FS), is highly favoured as an extension for expressing uncertainty through degrees of membership (η) and non-membership (υ). This article introduces novel measures for cosine similarity and distance in CFFSs. These measures are designed to improve the accuracy and efficiency of similarity and distance calculations in CFFSs. Also, a novel method is introduced for developing alternate similarity measures for CFFSs utilizing the proposed similarity measures that adhere to the similarity measures axiom. In addition, the connection between similarity and distance measures is utilized to construct a cosine distance metric for CFFSs. This newly suggested cosine similarity measure can not only provide solutions to decision-making problems from a geometric perspective but also from an algebraic point of view. To conclude, a case study is presented to showcase the practicality and effectiveness of the proposed approach, followed by a comparison of the outcomes of the suggested technique with some existing methodologies. This analysis helps to validate the proposed method and demonstrates its potential for outperforming other available approaches in terms of efficiency and accuracy. |
| first_indexed | 2024-03-13T05:30:16Z |
| format | Article |
| id | doaj.art-323c50e29fbe4d7091f5aa31b1f4aff3 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-03-13T05:30:16Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-323c50e29fbe4d7091f5aa31b1f4aff32023-06-15T04:54:21ZengElsevierAlexandria Engineering Journal1110-01682023-07-0173309319Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy setsMuhammad Rahim0Harish Garg1Fazli Amin2Luis Perez-Dominguez3Ahmed Alkhayyat4Department of Mathematics and Statistics, Hazara University, Mansehra, KP, PakistanSchool of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India; Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan; Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 248002, Uttarakhand, India; Corresponding author.Department of Mathematics and Statistics, Hazara University, Mansehra, KP, PakistanDepartamento de ingeniería industrial, Universidad Autónoma de Ciudad JuárezQaulity Assurance Department, The Islamic University, Najaf, IraqSimilarity and distance measures play important roles in fuzzy environments, helping to quantify the degree of similarity or concepts that may not have clear limits. They are used in various fields, including fuzzy logic, fuzzy clustering, and fuzzy decision-making. The cubic Fermatean fuzzy set (CFFS), which is a type of fuzzy set (FS), is highly favoured as an extension for expressing uncertainty through degrees of membership (η) and non-membership (υ). This article introduces novel measures for cosine similarity and distance in CFFSs. These measures are designed to improve the accuracy and efficiency of similarity and distance calculations in CFFSs. Also, a novel method is introduced for developing alternate similarity measures for CFFSs utilizing the proposed similarity measures that adhere to the similarity measures axiom. In addition, the connection between similarity and distance measures is utilized to construct a cosine distance metric for CFFSs. This newly suggested cosine similarity measure can not only provide solutions to decision-making problems from a geometric perspective but also from an algebraic point of view. To conclude, a case study is presented to showcase the practicality and effectiveness of the proposed approach, followed by a comparison of the outcomes of the suggested technique with some existing methodologies. This analysis helps to validate the proposed method and demonstrates its potential for outperforming other available approaches in terms of efficiency and accuracy.http://www.sciencedirect.com/science/article/pii/S111001682300340XCubic Fermatean fuzzy setsCosine similarity measureDistance measuresMCDMTOPSIS method |
| spellingShingle | Muhammad Rahim Harish Garg Fazli Amin Luis Perez-Dominguez Ahmed Alkhayyat Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets Alexandria Engineering Journal Cubic Fermatean fuzzy sets Cosine similarity measure Distance measures MCDM TOPSIS method |
| title | Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets |
| title_full | Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets |
| title_fullStr | Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets |
| title_full_unstemmed | Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets |
| title_short | Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets |
| title_sort | improved cosine similarity and distance measures based topsis method for cubic fermatean fuzzy sets |
| topic | Cubic Fermatean fuzzy sets Cosine similarity measure Distance measures MCDM TOPSIS method |
| url | http://www.sciencedirect.com/science/article/pii/S111001682300340X |
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