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Equilibrium Point of Representable Moore Continuous n-Dimensional Interval Fuzzy Negations

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Book cover Fuzzy Information Processing (NAFIPS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 831))

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Abstract

n-dimensional interval fuzzy sets are a type of fuzzy sets which consider ordered n-tuples in \([0,1]^n\) as membership degree. This paper considers the notion of representable n-dimensional interval fuzzy negations, in particular, these that are Moore continuous, proposed in a previous paper of the authors, and we study some conditions that guarantee the existence of equilibrium point in classes of representable (Moore continuous) n-dimensional interval fuzzy negations. In addition, we prove that the changing of the dimensions of representable Moore continuous n-dimensional fuzzy negations inherits their equilibrium points.

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Notes

  1. 1.

    In the literature on fuzzy negations had been widely used both terms for the same notion, namely, an element \(e\in [0,1]\) such that \(N(e)=e\), with N being a fuzzy negation. We choice “equilibrium point” over “fixed point” but this not means that we consider the term equilibrium point more correct or better than the fixed point.

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Acknowledgment

This work is supported by Brazilian National Counsel of Technological and Scientific Development CNPq (Proc. 307781/2016-0 and 404382/2016-9).

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Authors and Affiliations

  1. Center of Exact and Natural Sciences - CCEN, Rural Federal University of SemiArid - UFERSA, Mossoró, Rio Grande do Norte, Brazil

    Ivan Mezzomo & Thadeu Milfont

  2. Department of Informatics and Applied Mathematics - DIMAp, Federal University of Rio Grande do Norte - UFRN, Natal, Rio Grande do Norte, Brazil

    Benjamín Bedregal & Thadeu Milfont

Authors
  1. Ivan Mezzomo
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  2. Benjamín Bedregal
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  3. Thadeu Milfont
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Corresponding authors

Correspondence to Ivan Mezzomo , Benjamín Bedregal or Thadeu Milfont .

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Editors and Affiliations

  1. Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Guilherme A. Barreto

  2. Department of Statistics & Applied Mathematics, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Ricardo Coelho

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Mezzomo, I., Bedregal, B., Milfont, T. (2018). Equilibrium Point of Representable Moore Continuous n-Dimensional Interval Fuzzy Negations. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_23

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  • DOI: https://doi.org/10.1007/978-3-319-95312-0_23

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-95312-0

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