Abstract
This paper deals with some algebraic and set-theoretical properties of rough sets. Our considerations are based on the original conception of rough sets formulated by Pawlak [4, 5]. Let U be any fixed non-empty set traditionally called the universe and let R be an equivalence relation on U. The pair A = (U, R) is called the approximation space. We will call the equivalence classes of the relation R the elementary sets. We denote the family of elementary sets by U/R. We assume that the empty set is also an elementary set. Every union of elementary sets will be called a composed set. We denote the family of composed sets by ComR. We can characterize each set X ⊆ U using the composed sets [5].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Z. Bonikowski, A Certain Conception of the Calculus of Rough Sets, Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 412–421.
E. Bryniarski, A calculus of rough sets of the first order, Bull.Pol.Ac.: Math., vol. 37 (1989), pp. 71–78.
M. Gehrke, E. Walker, On the Structures of Rough Sets, Bull.Pol.Ac.: Math., vol. 40 (1992), pp. 235–245.
Z. Pawlak, Information systems. Theoretical foundations., WNT, Warszawa, 1983 (in Polish).
Z. Pawlak, Rough Sets. Theoretical Aspects of Reasoning about Data., Kluwer Academic Publisher, Dordrecht, 1991.
J. Pomykala, J.A. Pomykala, The Stone Algebra of Rough Sets, Bull. Pol.Ac.:Math., vol. 36 (1988), pp. 495–508.
H. Rasiowa, R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa, 1970.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 British Computer Society
About this paper
Cite this paper
Bonikowski, Z. (1994). Algebraic Structures of Rough Sets. In: Ziarko, W.P. (eds) Rough Sets, Fuzzy Sets and Knowledge Discovery. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3238-7_29
Download citation
DOI: https://doi.org/10.1007/978-1-4471-3238-7_29
Publisher Name: Springer, London
Print ISBN: 978-3-540-19885-7
Online ISBN: 978-1-4471-3238-7
eBook Packages: Springer Book Archive