Rough-fuzzy membership functions

This paper generalizes the concept of rough membership functions in pattern classification tasks to rough-fuzzy membership 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 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 membership functions are exploited to characterize the concept of rough-fuzzy sets and to measure the rough-fuzzy ambiguity associated with a given output class. Finally, a few possible applications of the rough-fuzzy membership functions are mentioned.