NEIGHBORHOOD SYSTEMS: A Qualitative Theory for Fuzzy and Rough Sets
نویسنده
چکیده
The theory of neighborhood systems is abstracted from the geometric notion of "near" or "negligible distances." It is a "new" theory of the classical concept of neighborhood systems within the context of advanced computing. By definition neighborhood systems include both rough sets and topological spaces as special cases. The deeper and more interesting part is in its interactions with fuzzy sets: Intuitively, qualitative fuzzy sets should be characterized by "elastic" membership functions that can tolerate “a small amount of continuous stretching with limited number of broken points.” Based on neighborhood systems we develop a theory for such qualitative fuzzy sets. As illustrations fuzzy inferences and Lyapunov stability are discussed.
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