Abstract
This paper generalizes the concept of rough membership functions in pattern classification tasks to rough–fuzzy membership functions and rough–fuzzy ownership functions. Unlike the rough membership value of a pattern, which is sensitive only towards the rough uncertainty associated with the pattern, the rough–fuzzy membership (or ownership) value of the pattern signifies the rough uncertainty as well as the fuzzy uncertainty associated with the pattern. In this paper, various set theoretic properties of the rough–fuzzy functions are exploited to characterize the concept of rough–fuzzy sets. These properties are also used to measure the rough–fuzzy uncertainty associated with the given output class. Finally, a few possible applications of the rough–fuzzy functions are mentioned.
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