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Two Classes of Entropy Measures for Complex Fuzzy Sets
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| Zeitschriftentitel: | Mathematics |
|---|---|
| Personen und Körperschaften: | , , , |
| In: | Mathematics, 7, 2019, 1, S. 96 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
MDPI AG
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| Schlagwörter: |
| author_facet |
Bi, Lvqing Zeng, Zhiqiang Hu, Bo Dai, Songsong Bi, Lvqing Zeng, Zhiqiang Hu, Bo Dai, Songsong |
|---|---|
| author |
Bi, Lvqing Zeng, Zhiqiang Hu, Bo Dai, Songsong |
| spellingShingle |
Bi, Lvqing Zeng, Zhiqiang Hu, Bo Dai, Songsong Mathematics Two Classes of Entropy Measures for Complex Fuzzy Sets General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) |
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bi, lvqing |
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Bi, Lvqing Zeng, Zhiqiang Hu, Bo Dai, Songsong 2227-7390 MDPI AG General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) http://dx.doi.org/10.3390/math7010096 <jats:p>Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.</jats:p> Two Classes of Entropy Measures for Complex Fuzzy Sets Mathematics |
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MDPI AG, 2019 |
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MDPI AG, 2019 |
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Mathematics |
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| title |
Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_unstemmed |
Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_full |
Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_fullStr |
Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_full_unstemmed |
Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_short |
Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_sort |
two classes of entropy measures for complex fuzzy sets |
| topic |
General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) |
| url |
http://dx.doi.org/10.3390/math7010096 |
| publishDate |
2019 |
| physical |
96 |
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<jats:p>Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.</jats:p> |
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| author | Bi, Lvqing, Zeng, Zhiqiang, Hu, Bo, Dai, Songsong |
| author_facet | Bi, Lvqing, Zeng, Zhiqiang, Hu, Bo, Dai, Songsong, Bi, Lvqing, Zeng, Zhiqiang, Hu, Bo, Dai, Songsong |
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| description | <jats:p>Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.</jats:p> |
| doi_str_mv | 10.3390/math7010096 |
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| imprint | MDPI AG, 2019 |
| imprint_str_mv | MDPI AG, 2019 |
| institution | DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Rs1, DE-Pl11, DE-105, DE-14, DE-Ch1, DE-L229 |
| issn | 2227-7390 |
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| language | English |
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| physical | 96 |
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| series | Mathematics |
| source_id | 49 |
| spelling | Bi, Lvqing Zeng, Zhiqiang Hu, Bo Dai, Songsong 2227-7390 MDPI AG General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) http://dx.doi.org/10.3390/math7010096 <jats:p>Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.</jats:p> Two Classes of Entropy Measures for Complex Fuzzy Sets Mathematics |
| spellingShingle | Bi, Lvqing, Zeng, Zhiqiang, Hu, Bo, Dai, Songsong, Mathematics, Two Classes of Entropy Measures for Complex Fuzzy Sets, General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous) |
| title | Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_full | Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_fullStr | Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_full_unstemmed | Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_short | Two Classes of Entropy Measures for Complex Fuzzy Sets |
| title_sort | two classes of entropy measures for complex fuzzy sets |
| title_unstemmed | Two Classes of Entropy Measures for Complex Fuzzy Sets |
| topic | General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous) |
| url | http://dx.doi.org/10.3390/math7010096 |