Abstract
To generalise the basic rough set definitions, the topology induced by equivalence relations is used. The proposed topological structure opens the way for the implementation of a broad range of topological facts and techniques in the granular computing process, including the introduction of the definition of topological membership functions that incorporates the concept of rough and fuzzy sets. There is an overlap between rough set theory and several other theories dealing with incomplete knowledge
Highlights
It is possible to consider rough set theory as a new mathematical method for imperfect data analysis
The Rough set theory has drawn the attention of many scientists and practitioners who have contributed to its development and applications
1.2 Definition The upper approximation of X with respect to R is the set of all objects that can be identified with certainty with respect to R as potential members of X
Summary
It is possible to consider rough set theory as a new mathematical method for imperfect data analysis. In many fields, such as decision support, engineering, the environment, finance, medicine and others, the theory has found applications. 1.2 Definition The upper approximation of X with respect to R is the set of all objects that can be identified with certainty with respect to R as potential members of X.
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