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Uncertainty Measurement for the Interval Type-2 Fuzzy Set

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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

In this paper, two measures of uncertainty for interval type-2 fuzzy sets are presented, evaluated, compared and contrasted. Wu and Mendel regard the length of the type-reduced set as a measure of the uncertainty in an interval set. Greenfield and John argue that the volume under the surface of the type-2 fuzzy set is a measure of the uncertainty relating to the set. For an interval type-2 fuzzy set, the volume measure is equivalent to the area of the footprint of uncertainty of the set. Experiments show that though the two measures give different results, there is considerable commonality between them. The concept of invariance under vertical translation is introduced; the uncertainty measure of a fuzzy set has the property of invariance under vertical translation if the value it generates remains constant under any vertical translation of the fuzzy set. It is left unresolved whether invariance under vertical translation is an essential property of a type-2 uncertainty measure.

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Author information

Authors and Affiliations

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

    Sarah Greenfield

Authors
  1. Sarah Greenfield
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Corresponding author

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. (2016). Uncertainty Measurement for the Interval Type-2 Fuzzy Set. 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_17

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  • DOI: https://doi.org/10.1007/978-3-319-39378-0_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39377-3

  • Online ISBN: 978-3-319-39378-0

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