Abstract
The paper presents an analysis of rough sets, rough top equality and rough bottom equality by means of pure logic-algebraic operations. Namely given an Approximation Space A, we can represent the induced rough sets structure as a particular Nelson algebra N(A) with a weak negation and a strong negation; in its turn N(A) can be viewed as a particular Heyting algebra equipped by its own pseudocomplementation. The relationships among these operations of negation reveal to fulfil some very peculiar properties that are able to provide the logic framework within which we can systematically deduce all the properties of rough (top, bottom) equalities.
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© 1994 British Computer Society
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Pagliani, P. (1994). A Pure Logic-algebraic Analysis of Rough Top and Rough Bottom Equalities. 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_27
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DOI: https://doi.org/10.1007/978-1-4471-3238-7_27
Publisher Name: Springer, London
Print ISBN: 978-3-540-19885-7
Online ISBN: 978-1-4471-3238-7
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