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Interval Type-2 Fuzzy Membership Function Generation Methods for Representing Sample Data

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Advances in Type-2 Fuzzy Sets and Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 301))

Abstract

Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than type-1 fuzzy sets (T1 FSs) in several areas of engineering. However, computing with T2 FSs can require an undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one. In this chapter, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means (IT2 FCM). For each method, the footprint of uncertainty (FOU) is only required to be obtained, since the FOU can completely describe an IT2 FMF. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.

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Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (Grant number 2011-0025655).

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Authors and Affiliations

  1. Computation Vision and Fuzzy Systems Laboratory, Department of Electronic and Communication Engineering, Hanyang University, 55 Hanyang Daehak-Ro, Sangnok-Gu, Ansan-Si, Gyeounggi-Do, 426-791, Korea

    Frank Chung-Hoon Rhee

  2. Strategic Sensor Group, Samsung Thales Co. Ltd, Yongin, Korea

    Byung-In Choi

Authors
  1. Frank Chung-Hoon Rhee
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  2. Byung-In Choi
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Correspondence to Frank Chung-Hoon Rhee .

Editor information

Editors and Affiliations

  1. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Alireza Sadeghian

  2. Hughes Aircraft Electrical Engineering B, Department of Electrical Engineering - S, University of Southern California, 3740 McClintock Ave., Los Angeles, 90089-2564, California, USA

    Jerry M. Mendel

  3. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Hooman Tahayori

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Rhee, F.CH., Choi, BI. (2013). Interval Type-2 Fuzzy Membership Function Generation Methods for Representing Sample Data. In: Sadeghian, A., Mendel, J., Tahayori, H. (eds) Advances in Type-2 Fuzzy Sets and Systems. Studies in Fuzziness and Soft Computing, vol 301. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6666-6_11

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  • DOI: https://doi.org/10.1007/978-1-4614-6666-6_11

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6665-9

  • Online ISBN: 978-1-4614-6666-6

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