# On the Lattice of Intervals and Rough Sets

Adam Grabowski; Magdalena Jastrzębska

Formalized Mathematics (2009)

- Volume: 17, Issue: 4, page 237-244
- ISSN: 1426-2630

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topAdam Grabowski, and Magdalena Jastrzębska. "On the Lattice of Intervals and Rough Sets." Formalized Mathematics 17.4 (2009): 237-244. <http://eudml.org/doc/267013>.

@article{AdamGrabowski2009,

abstract = {Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models deals with the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, here we rather concentrate on the model with the pair of two definable sets, hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [3], is also a step towards the formalization of the algebraic theory of rough sets, as in [4] or [9].},

author = {Adam Grabowski, Magdalena Jastrzębska},

journal = {Formalized Mathematics},

language = {eng},

number = {4},

pages = {237-244},

title = {On the Lattice of Intervals and Rough Sets},

url = {http://eudml.org/doc/267013},

volume = {17},

year = {2009},

}

TY - JOUR

AU - Adam Grabowski

AU - Magdalena Jastrzębska

TI - On the Lattice of Intervals and Rough Sets

JO - Formalized Mathematics

PY - 2009

VL - 17

IS - 4

SP - 237

EP - 244

AB - Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models deals with the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, here we rather concentrate on the model with the pair of two definable sets, hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [3], is also a step towards the formalization of the algebraic theory of rough sets, as in [4] or [9].

LA - eng

UR - http://eudml.org/doc/267013

ER -

## References

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- [6] Z. Pawlak. Rough sets. International Journal of Parallel Programming, 11:341-356, 1982, doi:10.1007/BF01001956.[Crossref] Zbl0501.68053
- [7] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
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- [9] Y. Y. Yao. Interval-set algebra for qualitative knowledge representation. Proc. 5-th Int. Conf. Computing and Information, pages 370-375, 1993.
- [10] Stanisław Żukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990.

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