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International Workshop on Fuzzy Logic and Applications

WILF 2016: Fuzzy Logic and Soft Computing Applications pp 3–26Cite as

Towards a Framework for Singleton General Forms of Interval Type-2 Fuzzy Systems

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10147))

Abstract

Recently, it has been shown that interval type-2 fuzzy sets (IT2FSs) are more general than interval-valued fuzzy sets (IVFSs), and some of these IT2FSs can actually be non-convex. Although these IT2FSs could be considered within the general type-2 fuzzy sets’ (GT2FSs) scope, this latter have always been studied and developed under certain conditions considering the convexity and normality of their secondary grades. In recent works the operations of intersection and union for GT2FSs have been extended to include non-convex secondary grades. Hence, there is a need to develop the theory for those general forms of interval type-2 fuzzy logic systems (gfIT2FLSs) which use IT2FSs that are not equivalent to IVFSs and can have non-convex secondary grades. In this chapter, we will present the mathematical tools to define the inference engine for singleton gfIT2FLSs. This work aims to introduce the basic structure of such singleton gfIT2FLSs, paying special attention to those blocks presenting significant differences with the already well known type-2 FLSs which employ IT2FSs which are equivalent to IVFSs (we will term IVFLSs).

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Notes

  1. 1.

    It should be noted that Eq. (7) has some similarity to Eq. (10) in [31] (see also [7]) as both equations refer to the join operation of general type-2 fuzzy sets. However, the representation of Eq. (7) is quite different to simplify the computations and analysis.

  2. 2.

    It should be noted that Eq. (31) has some similarity to Eq. (11) in [31] as both equations refer to the meet operation of general type-2 fuzzy sets. However, the representation of Eq. (31) is different to simplify the computations and analysis.

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Author information

Authors and Affiliations

  1. Department of Computer Architecture and Computer Technologies, Universidad de Granada, Granada, Spain

    Gonzalo Ruiz-García, Ignacio Rojas & Hector Pomares

  2. The Computational Intelligence Centre, School of Computer Science and Electronic Engineering, University of Essex, Colchester, UK

    Hani Hagras

Authors
  1. Gonzalo Ruiz-García
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  2. Hani Hagras
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  3. Ignacio Rojas
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  4. Hector Pomares
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Editor information

Editors and Affiliations

  1. University of Naples “Parthenope”, Naples, Italy

    Alfredo Petrosino

  2. University of Salerno, Fisciano, (Salerno), Italy

    Vincenzo Loia

  3. University of Alberta, Edmonton, Alberta, Canada

    Witold Pedrycz

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Ruiz-García, G., Hagras, H., Rojas, I., Pomares, H. (2017). Towards a Framework for Singleton General Forms of Interval Type-2 Fuzzy Systems. In: Petrosino, A., Loia, V., Pedrycz, W. (eds) Fuzzy Logic and Soft Computing Applications. WILF 2016. Lecture Notes in Computer Science(), vol 10147. Springer, Cham. https://doi.org/10.1007/978-3-319-52962-2_1

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  • DOI: https://doi.org/10.1007/978-3-319-52962-2_1

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