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A SSA-Based New Framework Allowing for Smoothing and Automatic Change-Points Detection in the Fuzzy Closed Contours of 2D Fuzzy Objects

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Modeling Decision for Artificial Intelligence (MDAI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6820))

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Abstract

The aim of this paper is to propose a new framework, based on Singular-Spectrum Analysis, allowing for smoothing and automatic change-point detection in the fuzzy closed contours of 2D fuzzy objects. The representation of fuzzy objects is first addressed, by distinguishing between fuzzy regions and fuzzy closed curves. Fuzzy shape signatures are derived in special cases, from which fuzzy time series can be subsequently sampled. Geodesic and Euclidean fuzzy paths and distances between two points in a fuzzy region are next contrasted. Finally, a novel approach to decomposing and reconstructing a fuzzy shape and to automatic change-point detection is proposed, based on a generalization of Singular-Spectrum Analysis so as to deal with complex-valued trajectory matrices. The coordinates themselves, represented as complex numbers are used as a shape signature. This approach is suitable for non-convex and non-star-shaped fuzzy contours.

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Author information

Authors and Affiliations

  1. Department of Mathematical Economics, University of Craiova, 13 A.I.Cuza str., 200585, Craiova, Romania

    Vasile Georgescu

Authors
  1. Vasile Georgescu
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Editor information

Editors and Affiliations

  1. Artificial Intelligence Research Institute (IIIA) Spanish National Research Council (CSIC), IIIA-CSIC, Campus Universitat Autonoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, Kunitachi, 184-0004, Tokyo, Japan

    Yasuo Narakawa

  3. School of Computer, National University of Defense Technology, 410073, Changsha, China

    Jianping Yin

  4. Department of Network Engineering, National University of Defense Technology, Yanwachi Street 137, 410073, Changsha, Hunan, China

    Jun Long

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© 2011 Springer-Verlag Berlin Heidelberg

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Georgescu, V. (2011). A SSA-Based New Framework Allowing for Smoothing and Automatic Change-Points Detection in the Fuzzy Closed Contours of 2D Fuzzy Objects. In: Torra, V., Narakawa, Y., Yin, J., Long, J. (eds) Modeling Decision for Artificial Intelligence. MDAI 2011. Lecture Notes in Computer Science(), vol 6820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22589-5_17

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  • DOI: https://doi.org/10.1007/978-3-642-22589-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22588-8

  • Online ISBN: 978-3-642-22589-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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