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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 2 > No. 1


Bi Operation and Rough Sets Generalizations

PP: 1-19
Heba I. Mustafa, A. M. Kozae, T. Y. Lin,
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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