Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle
We build a bridge between qualitative representation and quantitative representation using fuzzy qualitative trigonometry. A unit circle obtained from fuzzy qualitative representation replaces the quantitative unit circle. Namely, we have developed the concept of a qualitative unit circle from the v...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2018/8623465 |
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| _version_ | 1832566679195877376 |
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| author | M. Clement Joe Anand Janani Bharatraj |
| author_facet | M. Clement Joe Anand Janani Bharatraj |
| author_sort | M. Clement Joe Anand |
| collection | DOAJ |
| description | We build a bridge between qualitative representation and quantitative representation using fuzzy qualitative trigonometry. A unit circle obtained from fuzzy qualitative representation replaces the quantitative unit circle. Namely, we have developed the concept of a qualitative unit circle from the view of fuzzy theory using Gaussian membership functions, which play a key role in shaping the fuzzy circle and help in obtaining sharper boundaries. We have also developed the trigonometric identities based on qualitative representation by defining trigonometric functions qualitatively and applied the concept to fuzzy particle swarm optimization using α-cuts. |
| format | Article |
| id | doaj-art-5fbf42b69f1c4fb4a84241664afe7939 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-5fbf42b69f1c4fb4a84241664afe79392025-02-03T01:03:24ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2018-01-01201810.1155/2018/86234658623465Gaussian Qualitative Trigonometric Functions in a Fuzzy CircleM. Clement Joe Anand0Janani Bharatraj1Department of Mathematics, Hindustan Institute of Technology and Science (Deemed to be University), Chennai 603103, IndiaDepartment of Mathematics, Hindustan Institute of Technology and Science (Deemed to be University), Chennai 603103, IndiaWe build a bridge between qualitative representation and quantitative representation using fuzzy qualitative trigonometry. A unit circle obtained from fuzzy qualitative representation replaces the quantitative unit circle. Namely, we have developed the concept of a qualitative unit circle from the view of fuzzy theory using Gaussian membership functions, which play a key role in shaping the fuzzy circle and help in obtaining sharper boundaries. We have also developed the trigonometric identities based on qualitative representation by defining trigonometric functions qualitatively and applied the concept to fuzzy particle swarm optimization using α-cuts.http://dx.doi.org/10.1155/2018/8623465 |
| spellingShingle | M. Clement Joe Anand Janani Bharatraj Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle Advances in Fuzzy Systems |
| title | Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle |
| title_full | Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle |
| title_fullStr | Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle |
| title_full_unstemmed | Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle |
| title_short | Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle |
| title_sort | gaussian qualitative trigonometric functions in a fuzzy circle |
| url | http://dx.doi.org/10.1155/2018/8623465 |
| work_keys_str_mv | AT mclementjoeanand gaussianqualitativetrigonometricfunctionsinafuzzycircle AT jananibharatraj gaussianqualitativetrigonometricfunctionsinafuzzycircle |