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A Direct Approach for Determining the Switch Points in the Karnik–Mendel Algorithm

Chen, Chao; John, Robert; Twycross, Jamie; Garibaldi, Jonathan M.

Authors

Robert John robert.john@nottingham.ac.uk



Abstract

The Karnik-Mendel algorithm is used to compute the centroid of interval type-2 fuzzy sets, determining the switch points needed for the lower and upper bounds of the centroid, through an iterative process. It is commonly acknowledged that there is no closed-form solution for determining such switch points. Many enhanced algorithms have been proposed to improve the computational efficiency of the Karnik-Mendel algorithm. However, all of these algorithms are still based on iterative procedures. In this paper, a direct approach based on derivatives for determining the switch points without multiple iterations has been proposed, together with mathematical proof that these switch points are correctly determining the lower and upper bounds of the centroid. Experimental simulations show that the direct approach obtains the same switch points, but is more computationally efficient than any of the existing (iterative) algorithms. Thus, we propose that this algorithm should be used in any application of interval type-2 fuzzy sets in which the centroid is required.

Journal Article Type Article
Publication Date 2018-04
Journal IEEE Transactions on Fuzzy Systems
Print ISSN 1063-6706
Electronic ISSN 1941-0034
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 26
Issue 2
Pages 1079-1085
APA6 Citation Chen, C., John, R., Twycross, J., & Garibaldi, J. M. (2018). A Direct Approach for Determining the Switch Points in the Karnik–Mendel Algorithm. IEEE Transactions on Fuzzy Systems, 26(2), 1079-1085. https://doi.org/10.1109/tfuzz.2017.2699168
DOI https://doi.org/10.1109/tfuzz.2017.2699168
Keywords Karnik-Mendel algorithm, centroid, interval type-2, fuzzy sets, iterative, closed-form, direct approach
Publisher URL http://ieeexplore.ieee.org/document/7913651/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information (c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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