Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition
In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voti...
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| Format: | Article |
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MDPI AG
2018-06-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/6/193 |
| _version_ | 1811184115983056896 |
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| author | Kifayat Ullah Tahir Mahmood Naeem Jan |
| author_facet | Kifayat Ullah Tahir Mahmood Naeem Jan |
| author_sort | Kifayat Ullah |
| collection | DOAJ |
| description | In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed. |
| first_indexed | 2024-04-11T13:08:51Z |
| format | Article |
| id | doaj.art-fe558023992747b489f98f5cd8fbde5b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:08:51Z |
| publishDate | 2018-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fe558023992747b489f98f5cd8fbde5b2022-12-22T04:22:39ZengMDPI AGSymmetry2073-89942018-06-0110619310.3390/sym10060193sym10060193Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern RecognitionKifayat Ullah0Tahir Mahmood1Naeem Jan2Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics & Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics & Statistics, International Islamic University, Islamabad 44000, PakistanIn this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed.http://www.mdpi.com/2073-8994/10/6/193intuitionistic fuzzy setpicture fuzzy setspherical fuzzy setT-spherical fuzzy setsimilarity measurespattern recognition |
| spellingShingle | Kifayat Ullah Tahir Mahmood Naeem Jan Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition Symmetry intuitionistic fuzzy set picture fuzzy set spherical fuzzy set T-spherical fuzzy set similarity measures pattern recognition |
| title | Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition |
| title_full | Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition |
| title_fullStr | Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition |
| title_full_unstemmed | Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition |
| title_short | Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition |
| title_sort | similarity measures for t spherical fuzzy sets with applications in pattern recognition |
| topic | intuitionistic fuzzy set picture fuzzy set spherical fuzzy set T-spherical fuzzy set similarity measures pattern recognition |
| url | http://www.mdpi.com/2073-8994/10/6/193 |
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