| Autor: |
Sivakumar, Sangeetha, Sathish, Shakeela |
| Předmět: |
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| Zdroj: |
Mathematical Modelling of Engineering Problems; Jun2024, Vol. 11 Issue 6, p1672-1678, 7p |
| Abstrakt: |
A rough set theory (RST) was developed by Zdzislaw Pawlak to handle vagueness and uncertainty in data analysis. An approximation of a vague concept consists of two precise concepts a lower and an upper approximation. These approximations are two basic operations in rough set theory. An upper approximation contains all objects that may possibly belong to a concept, and a lower approximation contains all objects that certainly belong. The boundary region is the difference between the upper and lower approximations. Thus, rough set theory expresses vagueness by using a boundary region of a set rather than by using membership. By using the pair of sets, rough set theory extends traditional set theory by defining a subset of a universe. The properties of any set can be clearly understood if an algebraic structure is developed. This paper considers an approximation space with a finite universe and introduces a rough action by a symmetric group S | U | acting on all rough sets in this space. Also, we proved that the number of orbits of the symmetric group S | U | in rough sets is one. We then introduced the S | U |-submodule and proved that the kernel of rough homomorphism is a rough submodule. An example of how rough action can be used to find missing values in sample cancer data has also been provided. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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