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arXiv · 2004.03593

On lattice-ordered $t_{r}$-norms for type-2 fuzzy sets

Xinxing Wu·Guanrong Chen
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Abstract

In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered $t_{r}$-norm, which is not the convolution of $t$-norms on $[0, 1]$, is obtained. These results negatively answer two open problems posed by Walker and Walker in [15].

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Xinxing Wu, Guanrong Chen. 2020-04-07. On lattice-ordered $t_{r}$-norms for type-2 fuzzy sets. https://arxiv.org/abs/2004.03593

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