Some Properties of Rough Sets on Fuzzy Approximation Spaces and Applications

The notion of Rough sets introduced by Pawlak has been extended in many directions to enhance its modelling power. One such approach is to reduce the restriction of the base relation being an equivalence relation. Adding the flavour of fuzzy sets to it a fuzzy proximity relation was used to generate a fuzzy approximation space by De et al. in 1999 and hence the rough sets on fuzzy approximation spaces could be generated. These are much more general than the basic rough sets and also the rough sets defined on proximity relations. However, some of the results established in this direction by De et al. have been found to be faulty. In this paper we show through examples that the results are actually faulty and provide their correct versions. Also, we establish some more properties of these rough sets. A real life application is provided to show the application of the results.

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