Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications
In fuzzy set theory, the similarity measure is a significant device that measures the degree of correlation between two objects. An extension to intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS) have been widely employed in numerous disciplines. It is critical to investigate the similari...
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| Format: | Article |
| Language: | English |
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University of Belgrade
2024-01-01
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| Series: | Yugoslav Journal of Operations Research |
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| Online Access: | https://doiserbia.nb.rs/img/doi/0354-0243/2024/0354-02432400004A.pdf |
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| author | Arora Hari Darshan Kumar Vijay Naithani Anjali |
| author_facet | Arora Hari Darshan Kumar Vijay Naithani Anjali |
| author_sort | Arora Hari Darshan |
| collection | DOAJ |
| description | In fuzzy set theory, the similarity measure is a significant device that measures the degree of correlation between two objects. An extension to intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS) have been widely employed in numerous disciplines. It is critical to investigate the similarity measure of PFS. The study proposes the trigonometric function to suggest new similarity measures of PFS to handle the uncertainty that the existing similarity measures are unable to differentiate. Firstly, axiomatic descriptions of similarity measures for the proposed measures are proved. Then, an example is used to validate the proposed measures. Application to pattern recognition and medical diagnosis is also discussed in real-life scenarios. The validity of the suggested similarity measures is proved by comparing the results to the effectiveness of current equivalent similarity measures. Finally, a comparative study of these real-life examples reveals that the novel similarity measures are more flexible and dependable than the current similarity measures in dealing with various real application difficulties. |
| format | Article |
| id | doaj-art-ffdb1b3f74d241078bf053da8b2b7ec4 |
| institution | OA Journals |
| issn | 0354-0243 1820-743X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | University of Belgrade |
| record_format | Article |
| series | Yugoslav Journal of Operations Research |
| spelling | doaj-art-ffdb1b3f74d241078bf053da8b2b7ec42025-08-20T02:09:47ZengUniversity of BelgradeYugoslav Journal of Operations Research0354-02431820-743X2024-01-0134356958610.2298/YJOR220515004A0354-02432400004AImpact of trigonometric similarity measures for pythagorean fuzzy sets and their applicationsArora Hari Darshan0Kumar Vijay1Naithani Anjali2Department of Mathematics, Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, IndiaDepartment of Mathematics, Manav Rachna International Institute of Research & Studies, Faridabad, IndiaDepartment of Mathematics, Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, IndiaIn fuzzy set theory, the similarity measure is a significant device that measures the degree of correlation between two objects. An extension to intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS) have been widely employed in numerous disciplines. It is critical to investigate the similarity measure of PFS. The study proposes the trigonometric function to suggest new similarity measures of PFS to handle the uncertainty that the existing similarity measures are unable to differentiate. Firstly, axiomatic descriptions of similarity measures for the proposed measures are proved. Then, an example is used to validate the proposed measures. Application to pattern recognition and medical diagnosis is also discussed in real-life scenarios. The validity of the suggested similarity measures is proved by comparing the results to the effectiveness of current equivalent similarity measures. Finally, a comparative study of these real-life examples reveals that the novel similarity measures are more flexible and dependable than the current similarity measures in dealing with various real application difficulties.https://doiserbia.nb.rs/img/doi/0354-0243/2024/0354-02432400004A.pdfintuitionistic fuzzy sets (ifs)pythagorean fuzzy sets (pfs)similarity measurespattern recognitionmedical diagnosis |
| spellingShingle | Arora Hari Darshan Kumar Vijay Naithani Anjali Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications Yugoslav Journal of Operations Research intuitionistic fuzzy sets (ifs) pythagorean fuzzy sets (pfs) similarity measures pattern recognition medical diagnosis |
| title | Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications |
| title_full | Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications |
| title_fullStr | Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications |
| title_full_unstemmed | Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications |
| title_short | Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications |
| title_sort | impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications |
| topic | intuitionistic fuzzy sets (ifs) pythagorean fuzzy sets (pfs) similarity measures pattern recognition medical diagnosis |
| url | https://doiserbia.nb.rs/img/doi/0354-0243/2024/0354-02432400004A.pdf |
| work_keys_str_mv | AT aroraharidarshan impactoftrigonometricsimilaritymeasuresforpythagoreanfuzzysetsandtheirapplications AT kumarvijay impactoftrigonometricsimilaritymeasuresforpythagoreanfuzzysetsandtheirapplications AT naithanianjali impactoftrigonometricsimilaritymeasuresforpythagoreanfuzzysetsandtheirapplications |