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.
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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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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