On the Lattice of Intervals and Rough Sets

• Autorzy: Adam Grabowski , Magdalena Jastrzębska
• Języki publikacji: 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].

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2009
• Tom: 17
• Numer: 4
• Strony: 237-244

Daty

wydano

2009-01-01

online

2010-07-08

Twórcy

autor

Adam Grabowski

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

autor

Magdalena Jastrzębska

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

Bibliografia

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• [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.

Identyfikatory

DOI

10.2478/v10037-009-0030-x