Typical Characteristic-Based Type-2 Fuzzy C-Means Algorithm

• Published in: IEEE transactions on fuzzy systems Vol. 29; no. 5; pp. 1173 - 1187
• Main Authors: Yang, Xiyang, Yu, Fusheng, Pedrycz, Witold
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 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
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2020.2969907

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.