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Bi Operation and Rough Sets Generalizations |
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PP: 1-19 |
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Author(s) |
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Heba I. Mustafa,
A. M. Kozae,
T. Y. Lin,
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Abstract |
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| Generalization of rough set model is an important aspect of rough set theory research.
The problem to be discussed in this paper is to minimize the boundary region and this
requires a new approximation approach which increases lower approximation and decreases
upper approximation.We generalize both constructive and algebraic method for
the theory of rough sets. Instead of one operation used by Jarvinen [1], we use two
operations to define, in a lattice theoretical setting, two new mappings which mimic
the rough approximations called pairwise lower and pairwise upper approximations.
We studied the properties of these approximations by imposing different axioms on the
suggested two operations. Also properties of the ordered set of the pairwise lower and
upper of an element of a complete atomic Boolean lattice are investigated. Numerical
examples are given. Finally an experimental example is given showing that our generalizations
can help in expert system and using lower and upper approximations given in
this work will minimize the boundary region. This will decrease the uncertainty region
that help decision maker to get more accurate results. |
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