Similarity measure, entropy and distance measure of multiple sets
A multiple set is an extended version of a fuzzy set that simultaneously addresses an element’s multiplicity and uncertainty. In this paper, we define the approximate equality of multiple sets and study some relevant properties associated with it. We then apply the notion of approximation equality o...
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| Format: | Article |
| Language: | English |
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Ayandegan Institute of Higher Education,
2024-07-01
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| Series: | Journal of Fuzzy Extension and Applications |
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| Online Access: | https://www.journal-fea.com/article_202106_c4bc727ca727b1f1599adfb3fc582ce8.pdf |
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| _version_ | 1832577790250057728 |
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| author | Sanjitha Radhakrishnan Baiju Thankachan |
| author_facet | Sanjitha Radhakrishnan Baiju Thankachan |
| author_sort | Sanjitha Radhakrishnan |
| collection | DOAJ |
| description | A multiple set is an extended version of a fuzzy set that simultaneously addresses an element’s multiplicity and uncertainty. In this paper, we define the approximate equality of multiple sets and study some relevant properties associated with it. We then apply the notion of approximation equality of multiple sets to solve a pattern recognition problem. A novel class of similarity measures involving implication operators is introduced and the characteristics of approximate equality corresponding to these similarity measures are discussed. Further, we propose the concepts of σ-entropy, σ-distance measure, and σ-similarity measure of multiple sets and illustrate these with some examples. Finally, we define the theory of similarity measures between elements in multiple sets. |
| format | Article |
| id | doaj-art-1545e0f260e746a9998dd6fdd19e4d86 |
| institution | Kabale University |
| issn | 2783-1442 2717-3453 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Ayandegan Institute of Higher Education, |
| record_format | Article |
| series | Journal of Fuzzy Extension and Applications |
| spelling | doaj-art-1545e0f260e746a9998dd6fdd19e4d862025-01-30T15:07:12ZengAyandegan Institute of Higher Education,Journal of Fuzzy Extension and Applications2783-14422717-34532024-07-015341643310.22105/jfea.2024.445140.1387202106Similarity measure, entropy and distance measure of multiple setsSanjitha Radhakrishnan0Baiju Thankachan1Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India.Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India.A multiple set is an extended version of a fuzzy set that simultaneously addresses an element’s multiplicity and uncertainty. In this paper, we define the approximate equality of multiple sets and study some relevant properties associated with it. We then apply the notion of approximation equality of multiple sets to solve a pattern recognition problem. A novel class of similarity measures involving implication operators is introduced and the characteristics of approximate equality corresponding to these similarity measures are discussed. Further, we propose the concepts of σ-entropy, σ-distance measure, and σ-similarity measure of multiple sets and illustrate these with some examples. Finally, we define the theory of similarity measures between elements in multiple sets.https://www.journal-fea.com/article_202106_c4bc727ca727b1f1599adfb3fc582ce8.pdfmultiple setentropydistance measuresimilarity measureapproximate equalitypattern recognition |
| spellingShingle | Sanjitha Radhakrishnan Baiju Thankachan Similarity measure, entropy and distance measure of multiple sets Journal of Fuzzy Extension and Applications multiple set entropy distance measure similarity measure approximate equality pattern recognition |
| title | Similarity measure, entropy and distance measure of multiple sets |
| title_full | Similarity measure, entropy and distance measure of multiple sets |
| title_fullStr | Similarity measure, entropy and distance measure of multiple sets |
| title_full_unstemmed | Similarity measure, entropy and distance measure of multiple sets |
| title_short | Similarity measure, entropy and distance measure of multiple sets |
| title_sort | similarity measure entropy and distance measure of multiple sets |
| topic | multiple set entropy distance measure similarity measure approximate equality pattern recognition |
| url | https://www.journal-fea.com/article_202106_c4bc727ca727b1f1599adfb3fc582ce8.pdf |
| work_keys_str_mv | AT sanjitharadhakrishnan similaritymeasureentropyanddistancemeasureofmultiplesets AT baijuthankachan similaritymeasureentropyanddistancemeasureofmultiplesets |