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• # Artykuł - szczegóły

## Formalized Mathematics

2009 | 17 | 4 | 237-244

## On the Lattice of Intervals and Rough Sets

EN

### Abstrakty

EN
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].

237-244

wydano
2009-01-01
online
2010-07-08

### Twórcy

autor
• Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
• Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

### Bibliografia

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• [2] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
• [3] Adam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21-28, 2004.
• [4] Amin Mousavi and Parviz Jabedar-Maralani. Relative sets and rough sets. Int. J. Appl. Math. Comput. Sci., 11(3):637-653, 2001.
• [5] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
• [6] Z. Pawlak. Rough sets. International Journal of Parallel Programming, 11:341-356, 1982, doi:10.1007/BF01001956.[Crossref]
• [7] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
• [8] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [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.