The Lattice of Fuzzy Intervals and Sufficient Conditions for its Distributivity

Details The Lattice of Fuzzy Intervals and Sufficient Conditions for its Distributivity The Lattice of Fuzzy Intervals and Sufficient Conditions for its Distributivity

2002-06-17

arxiv.org/abs/cs/0206025v1

Computer Science

Other Computer Science

Scientific paper

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.

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