Abstract
Unit operations are some special functions on sets. The concept of the unit operation originates from researches of U.Wybraniec-Skardowska. The paper is concerned with the general properties of such functions. The isomorphism between binary relations and unit operations is proved. Algebraic structures of families of unit operations corresponding to certain classes of binary relations are considered. Unit operations are useful in Pawlak’s Rough Set Theory. It is shown that unit operations are upper approximations in approximation space. We prove, that in the approximation space (U,R) generated by a reflexive relation R the corresponding unit operation is the least definable approximation if and only if the relation R is transitive.
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Bonikowski, Z. (2010). Unit Operations in Approximation Spaces. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds) Rough Sets and Current Trends in Computing. RSCTC 2010. Lecture Notes in Computer Science(), vol 6086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13529-3_36
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DOI: https://doi.org/10.1007/978-3-642-13529-3_36
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