Typical Characteristic-Based Type-2 Fuzzy C-Means Algorithm
Type-2 fuzzy sets provide an efficient vehicle for handling uncertainties of real-world problems, including noisy observations. Bringing type-2 fuzzy sets to clustering algorithms offers more flexibility to handle uncertainties associated with membership concepts caused by a noisy environment. Howev...
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| Published in | IEEE transactions on fuzzy systems Vol. 29; no. 5; pp. 1173 - 1187 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1063-6706 1941-0034 |
| DOI | 10.1109/TFUZZ.2020.2969907 |
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| Abstract | Type-2 fuzzy sets provide an efficient vehicle for handling uncertainties of real-world problems, including noisy observations. Bringing type-2 fuzzy sets to clustering algorithms offers more flexibility to handle uncertainties associated with membership concepts caused by a noisy environment. However, the existing type-2 fuzzy clustering algorithms suffer from a time-consuming type-reduction process, which not only hampers the clustering performance but also increases the burden of understanding the clustering results. In order to alleviate the problem, this article introduces a set of typical characteristics of type-2 fuzzy sets and establishes a characteristic-based type-2 fuzzy clustering algorithm. Being different from the objective function used in the fuzzy C-means (FCM) algorithm that produces cluster centers and type-1 memberships, the objective function in the proposed algorithm contains additional characteristics of type-2 membership grades, namely, centers of gravity and cardinalities of the secondary fuzzy sets. The derived iterative formulas used for these parameters are much more efficient than the interval type-2 FCM algorithm. The experiments carried out in this study show that the proposed typical characteristic-based type-2 FCM algorithm has an ability of detecting noise as well as assigning suitable membership degrees to the individual data. |
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| AbstractList | Type-2 fuzzy sets provide an efficient vehicle for handling uncertainties of real-world problems, including noisy observations. Bringing type-2 fuzzy sets to clustering algorithms offers more flexibility to handle uncertainties associated with membership concepts caused by a noisy environment. However, the existing type-2 fuzzy clustering algorithms suffer from a time-consuming type-reduction process, which not only hampers the clustering performance but also increases the burden of understanding the clustering results. In order to alleviate the problem, this article introduces a set of typical characteristics of type-2 fuzzy sets and establishes a characteristic-based type-2 fuzzy clustering algorithm. Being different from the objective function used in the fuzzy C-means (FCM) algorithm that produces cluster centers and type-1 memberships, the objective function in the proposed algorithm contains additional characteristics of type-2 membership grades, namely, centers of gravity and cardinalities of the secondary fuzzy sets. The derived iterative formulas used for these parameters are much more efficient than the interval type-2 FCM algorithm. The experiments carried out in this study show that the proposed typical characteristic-based type-2 FCM algorithm has an ability of detecting noise as well as assigning suitable membership degrees to the individual data. |
| Author | Yang, Xiyang Pedrycz, Witold Yu, Fusheng |
| Author_xml | – sequence: 1 givenname: Xiyang orcidid: 0000-0002-9790-8992 surname: Yang fullname: Yang, Xiyang email: yangxiyang@139.com organization: Key Laboratory of Intelligent Computing and Information Processing of Fujian Province, Quanzhou Normal University, Quanzhou, China – sequence: 2 givenname: Fusheng orcidid: 0000-0001-9144-9150 surname: Yu fullname: Yu, Fusheng email: yufusheng@bnu.edu.cn organization: School of Mathematical Sciences, Beijing Normal University, Beijing, China – sequence: 3 givenname: Witold orcidid: 0000-0002-9335-9930 surname: Pedrycz fullname: Pedrycz, Witold email: wpedrycz@ualberta.ca organization: Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada |
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| SubjectTerms | Algorithms Cardinality center of gravity (COG) characteristics Clustering Clustering algorithms fuzzy clustering Fuzzy sets Linear programming Noise measurement Partitioning algorithms Phase change materials type-2 fuzzy sets (T2FS) Uncertainty |
| Title | Typical Characteristic-Based Type-2 Fuzzy C-Means Algorithm |
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