The Lattice of Fuzzy Intervals and Sufficient Conditions for its Distributivity
<|reference_start|>The Lattice of Fuzzy Intervals and Sufficient Conditions for its Distributivity: Given a reference lattice, we define fuzzy intervals to be the fuzzy sets such that their p-cuts are crisp closed intervals. We show that: given a complete reference lattice, the collection of its fuzzy intervals is a complete lattice. Furthermore we show that: if the reference lattice is completely distributive then the lattice of its fuzzy intervals is distributive.<|reference_end|>
@article{kehagias2002the,
    title={The Lattice of Fuzzy Intervals and Sufficient Conditions for its
  Distributivity},
    author={Ath. Kehagias},
    journal={arXiv preprint arXiv:cs/0206025},
    year={2002},
    archivePrefix={arXiv},
    eprint={cs/0206025},
    primaryClass={cs.OH}
}