Please use this identifier to cite or link to this item: https://doi.org/10.1109/FUZZ-IEEE.2012.6251178
Title: Modeling capability of type-1 fuzzy set and interval type-2 fuzzy set
Authors: Nie, M.
Tan, W.W. 
Keywords: Centroid
Interval type-2 fuzzy set
Karnik-Mendel type-reduction method
Modelling Capability
Issue Date: 2012
Source: Nie, M.,Tan, W.W. (2012). Modeling capability of type-1 fuzzy set and interval type-2 fuzzy set. IEEE International Conference on Fuzzy Systems : -. ScholarBank@NUS Repository. https://doi.org/10.1109/FUZZ-IEEE.2012.6251178
Abstract: Fuzzy logic (FL) has been regarded as a useful methodology in modelling. The modeling performance of FL heavily relies on the modeling capability of a fuzzy set (FS). However, the MF of a FS cannot be arbitrarily accurate in practice and thus the centroid as a measure of a FS cannot be accurate to any degree. In face of inaccurate MF, the sensitivity of the centroid of a FS to the deviation of its MF from the ideal MF determines the accuracy of the centroid. To evaluate the modeling capability of a type-1 (T1) FS and an interval type-2 (IT2) FS, this paper will present a comparative study of the sensitivity of the centroid of a T1 FS and an IT2 FS to the deviation of their MFs from the ideal MFs. In this paper, equations relating the amount that the centroid of a T1 FS and an IT2 FS vary with the deviation of their MFs from the ideal MFs were established. Based on the derived equations, it was found that an IT2 FS is able to provide an additional design freedom to vary the sensitivity of its centroid compared to a T1 FS. This unique characteristic may enable an IT2 FS to minimize the sensitivity of the centroid and thus to achieve higher modeling accuracy. Furthermore, guidelines for designing an IT2 FS were provided. © 2012 IEEE.
Source Title: IEEE International Conference on Fuzzy Systems
URI: http://scholarbank.nus.edu.sg/handle/10635/70987
ISBN: 9781467315067
ISSN: 10987584
DOI: 10.1109/FUZZ-IEEE.2012.6251178
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