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Slicing Strategies for the Generalised Type-2 Mamdani Fuzzy Inferencing System

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Artificial Intelligence and Soft Computing (ICAISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9692))

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Abstract

As a three-dimensional object, there are a number of ways of slicing a generalised type-2 fuzzy set. In the context of the Mamdani Fuzzy Inferencing System, this paper concerns three accepted slicing strategies, the vertical slice, the wavy slice, and the horizontal slice or \(\alpha \)-plane. Two ways of defining the generalised type-2 fuzzy set, vertical slices and wavy slices, are presented. Fuzzification and inferencing is presented in terms of vertical slices. After that, the application of all three slicing strategies to defuzzification is described, and their strengths and weaknesses assessed.

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Notes

  1. 1.

    The alternative is the Takagi-Sugeno-Kang FIS for which the output membership functions are either linear or constant; defuzzification is superfluous as the outputs may be aggregated via a simple weighted sum.

  2. 2.

    The optimised inferencing algorithms described in [11] employ vertical slices.

  3. 3.

    Discretisation in itself brings an unavoidable element of approximation. However the exhaustive method does not subsequently introduce further inaccuracies.

  4. 4.

    Independently of Liu, and at about the same time, Wagner and Hagras introduced the notion of zSlices [27], a concept very similar to that of \(\alpha \)-planes.

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Authors and Affiliations

  1. De Montfort University, Leicester, LE1 9BH, UK

    Sarah Greenfield & Francisco Chiclana

Authors
  1. Sarah Greenfield
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  2. Francisco Chiclana
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Correspondence to Sarah Greenfield .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Czestochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Czestochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Czestochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

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Greenfield, S., Chiclana, F. (2016). Slicing Strategies for the Generalised Type-2 Mamdani Fuzzy Inferencing System. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2016. Lecture Notes in Computer Science(), vol 9692. Springer, Cham. https://doi.org/10.1007/978-3-319-39378-0_18

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  • DOI: https://doi.org/10.1007/978-3-319-39378-0_18

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