Type-2 fuzzy elliptic membership functions for modeling uncertainty
Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs in mode...
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/49651/ |
| _version_ | 1848798047235997696 |
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| author | Kayacan, Erdal Sarabakha, Andriy Coupland, Simon John, Robert Khanesard, Mojtaba Ahmadieh |
| author_facet | Kayacan, Erdal Sarabakha, Andriy Coupland, Simon John, Robert Khanesard, Mojtaba Ahmadieh |
| author_sort | Kayacan, Erdal |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance with existing type-2 fuzzy MFs. Furthermore, fuzzy arithmetic operations are also investigated, and our finding is that the elliptic MF has similar features to the Gaussian and triangular MFs in addition and multiplication operations. Moreover, we have tested the prediction capability of elliptic MFs using interval type-2 fuzzy logic systems on oil price prediction problem for a data set from 2nd Jan 1985 till 25th April 2016. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem of a quadrotor. We believe that the results of this study will open the doors to elliptic MFs’ wider use of real-world identification and control applications as the proposed MF is easy to interpret in addition to its unique features. |
| first_indexed | 2025-11-14T20:13:33Z |
| format | Article |
| id | nottingham-49651 |
| institution | University of Nottingham Malaysia Campus |
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| last_indexed | 2025-11-14T20:13:33Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
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| spelling | nottingham-496512020-05-04T19:34:31Z https://eprints.nottingham.ac.uk/49651/ Type-2 fuzzy elliptic membership functions for modeling uncertainty Kayacan, Erdal Sarabakha, Andriy Coupland, Simon John, Robert Khanesard, Mojtaba Ahmadieh Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance with existing type-2 fuzzy MFs. Furthermore, fuzzy arithmetic operations are also investigated, and our finding is that the elliptic MF has similar features to the Gaussian and triangular MFs in addition and multiplication operations. Moreover, we have tested the prediction capability of elliptic MFs using interval type-2 fuzzy logic systems on oil price prediction problem for a data set from 2nd Jan 1985 till 25th April 2016. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem of a quadrotor. We believe that the results of this study will open the doors to elliptic MFs’ wider use of real-world identification and control applications as the proposed MF is easy to interpret in addition to its unique features. Elsevier 2018-04-30 Article PeerReviewed Kayacan, Erdal, Sarabakha, Andriy, Coupland, Simon, John, Robert and Khanesard, Mojtaba Ahmadieh (2018) Type-2 fuzzy elliptic membership functions for modeling uncertainty. Engineering Applications of Artificial Intelligence, 70 . pp. 170-183. ISSN 0952-1976 Elliptic membership function type-2 fuzzy logic theory uncertainty fuzzy sets Gaussian triangular addition multiplication fuzzy arithmetics https://www.sciencedirect.com/science/article/pii/S0952197618300253 doi:10.1016/j.engappai.2018.02.004 doi:10.1016/j.engappai.2018.02.004 |
| spellingShingle | Elliptic membership function type-2 fuzzy logic theory uncertainty fuzzy sets Gaussian triangular addition multiplication fuzzy arithmetics Kayacan, Erdal Sarabakha, Andriy Coupland, Simon John, Robert Khanesard, Mojtaba Ahmadieh Type-2 fuzzy elliptic membership functions for modeling uncertainty |
| title | Type-2 fuzzy elliptic membership functions for modeling uncertainty |
| title_full | Type-2 fuzzy elliptic membership functions for modeling uncertainty |
| title_fullStr | Type-2 fuzzy elliptic membership functions for modeling uncertainty |
| title_full_unstemmed | Type-2 fuzzy elliptic membership functions for modeling uncertainty |
| title_short | Type-2 fuzzy elliptic membership functions for modeling uncertainty |
| title_sort | type-2 fuzzy elliptic membership functions for modeling uncertainty |
| topic | Elliptic membership function type-2 fuzzy logic theory uncertainty fuzzy sets Gaussian triangular addition multiplication fuzzy arithmetics |
| url | https://eprints.nottingham.ac.uk/49651/ https://eprints.nottingham.ac.uk/49651/ https://eprints.nottingham.ac.uk/49651/ |