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dc.contributor.authorGrabowski, Adam-
dc.identifier.citationFormalized Mathematics, Volume 21, Issue 1, 2013, Pages 55-64-
dc.description.abstractThe notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based models of rough sets [12] trying to formalize some parts of [19] following also [18] in some sense (Propositions 1-8, Corr. 1 and 2; the complete description is available in the Mizar script). Our main problem was that informally, there is a direct correspondence between relations and underlying properties, in our approach however [7], which uses relational structures rather than relations, we had to switch between classical (based on pure set theory) and abstract (using the notion of a structure) parts of the Mizar Mathematical Library. Our next step will be translation of these properties into the pure language of Mizar attributes.-
dc.publisherDe Gruyter Open-
dc.titleRelational Formal Characterization of Rough Sets-
dc.description.AffiliationInstitute of Informatics University of Białystok Akademicka 2, 15-267 Białystok, Poland-
dc.description.referencesCzesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.-
dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
dc.description.referencesCzesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
dc.description.referencesCzesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
dc.description.referencesAdam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21-28, 2004.-
dc.description.referencesAdam Grabowski and Magdalena Jastrzebska. A note on a formal approach to rough operators. In Marcin S. Szczuka and Marzena Kryszkiewicz et al., editors, Rough Setsand Current Trends in Computing - 7th International Conference, RSCTC 2010, Warsaw,Poland, June 28-30, 2010. Proceedings, volume 6086 of Lecture Notes in ComputerScience, pages 307-316. Springer, 2010. doi:10.1007/978-3-642-13529-333.-
dc.description.referencesArtur Korniłowicz. Cartesian products of relations and relational structures. Formalized Mathematics, 6(1):145-152, 1997.-
dc.description.referencesBeata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.-
dc.description.referencesZ. Pawlak. Rough sets. International Journal of Parallel Programming, 11:341-356, 1982. doi:10.1007/BF01001956.-
dc.description.referencesKonrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.-
dc.description.referencesAndrzej Skowron and Jarosław Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245-253, 1996. doi:10.3233/FI-1996-272311.-
dc.description.referencesAndrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115-122, 1990.-
dc.description.referencesWojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.-
dc.description.referencesMirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.-
dc.description.referencesY.Y. Yao. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning, 15(4):291-317, 1996. doi:10.1016/S0888-613X(96)00071-0.-
dc.description.referencesWilliam Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997-5011, 2007.
Występuje w kolekcji(ach):Artykuły naukowe (WMiI)
Formalized Mathematics, 2013, Volume 21, Issue 1

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