On primal ideal approximation spaces
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In this paper, we introduce ``primal ideal'' to generate new closure operators and, thus, new spaces named primal ideal approximation spaces. Some topological notions such as accumulation points, lower separation axioms, and connectedness in these primal ideal approximation spaces are defined and studied. Some examples are given to confirm the implications. Improving the accuracy measure and reducing the boundary region can be achieved easily by utilizing primal ideal in the construction of the approximations as it plays an important role in removing the vagueness of concept. The emergence of primal ideals leads to increase the lower approximations and decrease the upper approximations. Consequently, it minimizes the boundary and makes the accuracy higher than the previous based on ideals. Finally, a real life application induced from an information system is introduced to demonstrate the importance of this paper.
Abstract
In this paper, we introduce ``primal ideal'' to generate new closure operators and, thus, new spaces named primal ideal approximation spaces. Some topological notions such as accumulation points, lower separation axioms, and connectedness in these primal ideal approximation spaces are defined and studied. Some examples are given to confirm the implications. Improving the accuracy measure and reducing the boundary region can be achieved easily by utilizing primal ideal in the construction of the approximations as it plays an important role in removing the vagueness of concept. The emergence of primal ideals leads to increase the lower approximations and decrease the upper approximations. Consequently, it minimizes the boundary and makes the accuracy higher than the previous based on ideals. Finally, a real life application induced from an information system is introduced to demonstrate the importance of this paper.
참고문헌 (24)
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