A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition
As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity deg...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/384241 |
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| _version_ | 1832552673866416128 |
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| author | Yafei Song Xiaodan Wang Lei Lei Aijun Xue |
| author_facet | Yafei Song Xiaodan Wang Lei Lei Aijun Xue |
| author_sort | Yafei Song |
| collection | DOAJ |
| description | As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns. |
| format | Article |
| id | doaj-art-e457940c02aa4883b7c04b238863875b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e457940c02aa4883b7c04b238863875b2025-02-03T05:58:13ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/384241384241A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern RecognitionYafei Song0Xiaodan Wang1Lei Lei2Aijun Xue3School of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, ChinaSchool of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, ChinaSchool of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, ChinaSchool of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, ChinaAs a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.http://dx.doi.org/10.1155/2014/384241 |
| spellingShingle | Yafei Song Xiaodan Wang Lei Lei Aijun Xue A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition Abstract and Applied Analysis |
| title | A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition |
| title_full | A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition |
| title_fullStr | A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition |
| title_full_unstemmed | A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition |
| title_short | A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition |
| title_sort | new similarity measure between intuitionistic fuzzy sets and its application to pattern recognition |
| url | http://dx.doi.org/10.1155/2014/384241 |
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