The reduction of interval type-2 LR fuzzy sets

Chao Lieh Chen, Shen Chien Chen, Yau Hwang Kuo

研究成果: Article

14 引文 斯高帕斯(Scopus)

摘要

Type reduction of interval type-2 (IT2) fuzzy sets is essential in conducting the type-2 fuzzy sets expressed with the resolution forms of IT2 fuzzy sets. Several type reduction methods, such as KM, EKM, and centroid flow, have been proposed. These methods are relatively easy to implement but still computation-intensive because they need to invoke an iterative switching point finding procedure. This study derives a theorem and proposes a heuristic algorithm, which can fast and accurately identify the minimum and maximum switching points of a piecewise smooth IT2 fuzzy set. It also demonstrates that it is easy to derive the close-form expressions of the switching points of a piecewise smooth IT2 fuzzy set if both of its upper and lower membership functions can be parameterized as LR fuzzy sets, which are defined in this paper. Then, the type reduction of piecewise smooth IT2 fuzzy sets can be simplified to solve the close-form expressions of their switching points in terms of LR parameters. Experiments on IT2 fuzzy sets with various piecewise smooth membership functions, including linear, Gaussian, and hybrid-shaped ones were made. The results showed that the proposed type reduction method can obtain solutions which accurately approximate to the desired switching points with much lower computational overhead than the Karnik-Mondel (KM) and enhanced KM (EKM) methods.

原文English
文章編號6576860
頁(從 - 到)840-858
頁數19
期刊IEEE Transactions on Fuzzy Systems
22
發行號4
DOIs
出版狀態Published - 2014 八月

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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